Papers by Area

Approximate CV

This is not up to date!!!
I update my publications every 10 years or so. It's possible I omitted things.
Titles are approximate and the last few papers' titles might change!
Oh well,,,,, Here it is.

Publications by Area

William J. Layton
Professor of Mathematics
Department of Mathematics
University of Pittsburgh
wjl@pitt.edu
http://www.math.pitt.edu/~wjl

Current Research Interests
1. Turbulence and large eddy simulation
2. Long time behavior of numerical methods and reduced models
3. Computational Fluid Dynamics and Applications
4. Numerical Analysis of Partial Differential Equations
5. Parallel and Adaptive Finite Element Algorithms

Research Publications Areas:
There are many ways to slice a pie.
Here is a rough division of my work into areas with lots of overlaps
and lots of different formats.
(I haven't listed "numerical analysis" or "finite element methods";
these are themes that run through most of the papers.)

Areas:
Hyperbolic equations and systems:
Near wall laws / Weak imposition of boundary conditions:
Finite difference methods
Defect Correction Methods
Numerical Analysis of convection diffusion problems
Thermohydraulics / Natural Convection Problems
Domain Decomposition and massively parallel algorithms
Two-level and Multi-level Methods
A Posteriori Error estimation and adaptivity
Variational Multiscale Methods
Large Eddy Simulation
Nonlinear PDEs: Analysis and Applications
Aluminum Reduction Cell Modeling and Simulation
Graph Theoretic Algorithms and Load Balancing
Porous media and Coupled Stokes-Darcy flow
Variational Inequalities
Linear and Nonlinear elliptic equations
MHD: Magneto-Hydrodynamics
Almost Periodic functions
Education in Computational Science and Engineering
Nonlinear Delay Equations

Hyperbolic equations and systems:
W. Layton,
The Galerkin Method for First Order Hyperbolic Equations ,
Ph.D. dissertation ,1980 University of Tennessee

Estimates Away from a Discontinuity for Dissipative Galerkin Methods
for Hyperbolic Equations ,
Math. of Comp. , 36 , 1981 pages 87--92 , MR 82b: 65129.

W. Layton,
Simplified L^ infinity Estimates for Finite Difference
Approximations to Hyperbolic Equations Proc. A.M.S. , 86 yr
1982 pages 491--495 , MR 94a: 65080

M. Gunzburger and W. Layton,
Numerical Boundary Conditions for Hyperbolic Systems,
Proc. Army Num. Anal. and Computers Conf. , 1981 pages 221--232

W. Layton,
Galerkin Methods for Two-Point Boundary Value Problems for First
Order Systems ,
SIAM J. Numer. Anl. , 20 yr 1983 pages 161-171 , MR
84d: 65059

W. Layton,
Stable Galerkin Methods for Hyperbolic Systems , SIAM J. Numer.
Anal. , 20 , 1983 pages 221--233 , MR 95c: 65120

W. Layton,
Stable and Unstable Numerical Boundary Conditions for Galerkin
Approximations to Hyperbolic Systems ,
Comp. and Math. With Applications , 9 , 1983 pages 559--566
, MR 94d:65054

W. Layton,
The Finite Element Method for a Degenerate Hyperbolic Partial
Differential Equation ,
B.I.T. , 23 , 1983 pages 231--238 , MR 84f: 65073

W. Layton,
Error Estimates for Finite Difference Approximations to Hyperbolic
Equations for Large Time Proc. A.M.S. , 92 yr 1984 pages
425--431 , MR 86h: 65135

W. Layton,
Some Effects of Numerical Integration in Finite Element
Approximations to Degenerate Evolution Equations Calcolo , 21
, 1984 pages 45--60

W. Layton,
On the Behavior Over Long Time Intervals of Finite Difference and
Finite Element Approximations to Hyperbolic Equations Comp. and Math.
with Appls , 11 , 1985 pages 93--112 , MR 86g: 65176

L. Drager, W. Layton,and R. Mattheij,
Asymptotics of Numerical Methods for Nonlinear Evolution Equations
in: Proc. VI Int. Conf. on Trends in Thy. and Practice of
Nonlinear Anal. , North-Holland Publishing Co. (1984), 131-136

W. Layton,
An Energy Analysis of a Degenerate Hyperbolic Partial Differential
Equations Aplikace Matematiky , 29 yr 1984 pages 350--366 , MR 86d: 35092

W. Layton,
On the Convergence of Spectral Methods for Semilinear Hyperbolic
Equations Numerical Functional Analysis and Optimitation , 7 , 1984 pages 303--310 , MR 86i: 65057

W. Layton,
High Accuracy Finite Element Methods for Positive Symmetric Systems
Comp. and Math. W. Appls. , 12 , 1986 pages 565--579

Quian Du, M. Gunzburger and W Layton ,
Low Dispersion, High Accuracy Finite Element Method for Hyperbolic
Systems in Several Space Variables ,
V15 , 1988 pages 447--457 Computers and Mathematics with Applications

W. Layton and Q. Du and M. Gunzburger
A nonstandard method of higher accuracy for hyperbolic systems in
several space variables,
Advances in Computer Methods for P.D.E.'s., IV, IMACS pages 92-97 , 1989

W. Layton,
On the Principle Axes of Diffusion in Difference Schemes for 2-D
Transport Problems, 90 , 1990 J. Computational Physics

W. Layton
Superconvergence of finite element discretization of time relaxation models of advection,
to appear: BIT, 2006.

Near wall laws / Weak imposition of boundary conditions:
For hyperbolic systems:

M. Gunzburger and W. Layton,
Numerical Boundary Conditions for Hyperbolic Systems Proc. Army
Num. Anal. and Computers Conf. , 1981 pages 221--232

W. Layton,
Stable and Unstable Numerical Boundary Conditions for Galerkin
Approximations to Hyperbolic Systems Comp. and Math. With Applications , 9 , 1983 pages 559--566 , MR
94d:65054

W. Layton,
Stable Galerkin Methods for Hyperbolic Systems , SIAM J. Numer.
Anal. , 20 , 1983 pages 221--233 , MR 95c: 65120

For fluid flow problems:

Weak imposition of ``no-slip'' boundary conditions in the finite
element method, Computers and Math. with Appls. , 38 , 1999 pages 129-142

A. Dunca, v. John, W. Layton and N. Sahin,
Numerical analysis of large eddy simulation,
359-364 in: DNS/LES progress and challenges (editors: C. Liu, L. Sakeland and T. Beutner) Greyden press, Columbus, 2001.

A. Dunca, V. John, W.J. Layton,
"The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain",
in G.P. Galdi, J.G. Heywood, R. Rannacher (Eds.), Contributions to
Current Challenges in Mathematical Fluid Mechanics, Advances in
Mathematical Fluid Mechanics 3, Birkhеser Verlag Basel, 53 - 78, 2004

. V. John, W. Layton and N. Sahin,
Derivation and analysis of near wall models for channel and
recirculating flows,
Computers and mathematics with applications,48[2004]1135-1151.

Finite difference methods

W. Layton,
Simplified L^ infinity Estimates for Finite Difference
Approximations to Hyperbolic Equations Proc. A.M.S. , 86 yr 1982 pages 491--495 , MR 94a: 65080

W. Layton,
Error Estimates for Finite Difference Approximations to Hyperbolic
Equations for Large Time Proc. A.M.S. , 92 yr 1984 pages
425--431 , MR 86h: 65135

W. Layton,
On Nonlinear Difference Approximations to Nonlinear Functional
Differential Equations with L. Drager Libertas Math. , 3 , 1983 pages 45--65 , MR85j: 34165

L. Drager and W. Layton,
Non-linear Delay Differential Equations and Function Algebras , in:
Proc. Int. Conf. on Diff. Eqns. eds I. Knowles and R. Lewis ,
North-Holland Publishing Co., 1983 pages 149--154 , MR 86i: 34089

W. Layton,
On the Behavior Over Long Time Intervals of Finite Difference and
Finite Element Approximations to Hyperbolic Equations Comp. and Mth. with Appls , 11 , 1985 pages 93--112 , MR 86g: 65176

L. Drager, W. Layton,and R. Mattheij,
Asymptotics of Numerical Methods for Nonlinear Evolution Equations
in: Proc. VI Int. Conf. on Trends in Thy. and Practice of Nonlinear
Anal. , North-Holland Publishing Co. (1984), 131-136

W Layton and T. Morley,
On Central Difference Approximations to General Second Order Elliptic ,
Linear Algebra and its Applications , 97 , 1987 pages 65--75

W. Layton,
On the Principle Axes of Diffusion in Difference Schemes for 2-D Transport Problems,
90 , 1990 J. Computational Physics

Optimal difference Schemes for 2-D transport problems , J. Comp.
Appl. Math. , 45 pages 337-341 , 1993

with V. Ervin
A robust and parallel relaxation method based on algebraic splittings
Numer. Methods for PDE's , 15 , 1999 pages 91-110

Defect Correction Methods

V Ervin and W Layton,
High Resolution, Minimal Storage Algorithms for Convection Dominated
Convection-Diffusion Equations,
in: Trans of the Fourth Army Conf. on Appl. Math. and Comp. , 1987 pages 1173--1201

V Ervin and W Layton,
A Study of Defect Correction, Finite Difference Methods for
Convection Diffusion Equations SIAM J. Numerical Analysis , 26 , 1989 pages 169--179

O Axelsson and W Layton,
Defect Correction Methods for Convection Dominated, Convection
Diffusion Equation,
1990 , 24 pages 423--455 R.A.I.R.O. J. Numer. Anal. (now M^2A.N.)

Iterative Methods as Discretization Procedures
with O. Axelsson
in: Preconditioned Conjugate Gradient Methods eds O. Axelsson and L. Yu Kolotilina Springer LNM , 1457 ,
Springer , Berlin , 1991 in: Springer L.N.M.

with V. Ervin and J. Maubach
Adaptive defect correction approach for convection dominated,
convection diffusion problems CTAC95, World Scientific,
Computational Techniques and Applications , 1995 pages 1-8

with V. Ervin and J. Maubach
Adaptive defect correction methods for viscous incompressible flow problems ,
SIAM J.N.A. 37[2000]1165-1185.

W. Layton and H.K. Lee and J. Peterson ,
A defect-correction method for the incompressible Navier-Stokes equations,
Applied Math and Computing, 129[2002]1-20.

S. Kaya, W. Layton and B. Riviere,
Subgrid stabilized defect correction methods for the Navier-Stokes equations ,
SIAM JNA 44 [2006] 1639.

Numerical Analysis of convection diffusion problems

V Ervin and W Layton,
High Resolution, Minimal Storage Algorithms for Convection Dominated
Convection-Diffusion Equations ,
in: Trans of the Fourth Army Conf. on Appl. Math. and Comp. , 1987 pages 1173--1201

V. Ervin and W Layton,
A Second Order Accurate, Positive Scheme for Singularly Perturbed Boundary Value Problems,
Comp. Mechanics , 3 , 1988 pages 115--128

V Ervin and W Layton,
On the Approximation of Derivatives of Singularly Perturbed Boundary Value Problems
, V8 , 1987 pages 265--277 SIAM J. Sci. Stat Computing

V Ervin and W Layton,
A Study of Defect Correction, Finite Difference Methods for Convection Diffusion Equations
SIAM J. Numerical Analysis , 26 , 1989 pages 169--179

O Axelsson and W Layton,
Defect Correction Methods for Convection Dominated, Convection Diffusion Equation,
1990 , 24 pages 423--455 R.A.I.R.O. J. Numer. Anal. (now M^2A.N.)

W. Layton,
On the Principle Axes of Diffusion in Difference Schemes for 2-D Transport Problems,
90 , 1990 J. Computational Physics

Iterative Methods as Discretization Procedures with O. Axelsson
in: Preconditioned Conjugate Gradient Methods eds O. Axelsson and L. Yu Kolotilina Springer LNM , 1457 ,
Springer , Berlin , 1991 in: Springer L.N.M.

with B. Polman,
Oscillation absorption finite element methods for convection diffusion problems ,
SIAM J.Scientific Computing , 17 , 1996 pages 1328-1346

with J. Maubach and P. Rabier
Robustness of an element wise parallel finite element method
for convection-diffusion problems
SIAM J. Scien. Computing , 19 , 1998 pages 1870-1891

with V. Ervin
A robust and parallel relaxation method based on algebraic splittings
Numer. Methods for PDE's , 15 , 1999 pages 91-110

with V. Ervin and J. Maubach
Adaptive defect correction approach for convection dominated, convection diffusion problems
CTAC95, World Scientific, Computational Techniques and Applications , 1995 pages 1-8

W. Layton and M. Cawood, V. Ervin and J. Maubach ,
Residual estimators for convection dominated, convection diffusion equations
J. Comp. Applied Math. v.116 , 2000 ,1-22

V John, S Kaya and W Layton,
A two-level variational multiscale method for convection diffusion equations,
Comp. Meth. Appl. Mech. Engrg., 195, 4594-4603, 2006.

W Layton,
A remark on regularity of an elliptic-elliptic singular perturbation problem,
technical report, 2007.

Thermohydraulics / Natural Convection Problems
J. Boland, G.B. Ermentrout, C.A. Hall, W Layton and H. Melhem
, Analytical and Numerical Studies of Natural Convection
Proc. Int. Conf. on Thy. and Appls. of Diff. Eqns. , 1988

J Boland and W Layton,
An Analysis of the Finite Element Method for Natural Convection Problems
Num. Meth. For P.D.E's , 2 , 1990 pages 115--126

with J. Boland
Error Analysis of Finite Element Methods in Steady Natural Convection Problems
Num. Functional Anal. and Optimization , 11 , 1990 pages 449--483

Domain Decomposition and massive parallel algorithms

with P. Rabier ,
Domain Decomposition via Operator Splitting for Nonsymmetric Problems
Appl. Math. Lett. , V5 , 1992 pages 67--70

Domain Decomposition for Multi-Dimensional, First Order Systems of Partial Differential Equations
Applicable Analysis , 47 (No. 2-3) pages 139-150 , 1992

with J. Maubach, P. Rabier and A. Sunmonu ,
Parallel Finite Element Methods,
in: Proc. 5th ISMM Conf. on Parallel and Distributed Computing and Systems , 1992

with V. Ervin and J. Maubach,
Some graph coloring problems in parallel numerical methods
in: Algorithms in de Algebra (A.H. M. Levelt, ed.)
Univ. of Nijmegen, the Netherlands pages 39 48 yr 1993

with R. Jeurissen ,
Load balancing via graph coloring: an algorithm
Computers Math. Applic. , 27 (No. 3) pages 27-32 , 1994

with J. Maubach and P. Rabier,
Robust methods for highly nonsymmetric problems,
Contemporary Mathematics , 180 , 1994

with P. Rabier,
Peaceman-Rachford Procedures and Domain Decomposition for Finite Element Problems
, J. Numer. Lin. Algb. and Appls. , 2 , 1995 pages 363-394

with J. Maubach and P.J. Rabier ,
Parallel algorithms for maximal monotone operators of local type
Numer. Math. , 71 , 1995 pages 29-58

with P.J. Rabier,
The element separation property and parallel finite element methods for the Navier--Stokes equations
Appl. Math. Ltrs. , 8 , 1995 pages 97-102

with J. Maubach and P. Rabier
Robustness of an element wise parallel finite element method for convection-diffusion problems
SIAM J. Scien. Computing , 19 , 1998 pages 1870-1891

with V. Ervin
A robust and parallel relaxation method based on algebraic splittings
Numer. Methods for PDE's , 15 , 1999 pages 91-110

Two and Multi-level Methods

A two level discretization method for the Navier-Stokes equations,
Comput. Math. Appl. , 26 pages 33-38 , 1993

with W. Lenferink and J. Peterson,
A two-level Newton, finite element algorithm for approximating electrically conducting,
incompressible fluid flows ,
Computers Math. Appls. , 28 yr 1994 pages 21-31

with W. Lenferink,
Two-level, Picard-defect corrections for the Navier-Stokes,
Applied Math. and Computing , 80 , 1995 pages 1-12

Solution algorithms for incompressible viscous flows at high Reynolds number,
Vestnik Mosk. Gos. Univ. (Computational Math. and Cybernetics)
series , 15 no. 1 , 1996 pages 25-35

with W. Lenferink
A multilevel mesh independence principle for the Navier-Stokes equations
SIAM J.N.A. , 33 , 1996 pages 17-30

with X. Ye,
Two-level discretizations for the stream function form of the Navier-Stokes equations
Num. Funct. Anal. and Appls., v. 20 , 1999 pages 909-917

with X. Ye,
Nonconforming two level discretizations of the stream function form of the Navier Stokes equations
Applied Math. and Comp. , 89 , 1998 pages 173-183

with V. Ervin and J. Maubach
A posteriori error estimation for a two level finite element method for the Navier-Stokes equations
Num. Meth. For P.D.E.'s , 12 , 1996 pages 333-346

with O. Axelsson,
A two-level discretization of nonlinear boundary value problems,
SIAM J.N.A. , 33 , 1996 pages 2359-2374

with L. Tobiska
A two-level method with backtracking for the Navier-Stokes equations
SIAM J.N.A. , 35 , 1998 pages 2035-2054

with H. Kwon Lee and J. Peterson
Numerical solution for the stationary Navier-Stokes equations by a multi level finite element method ,
SIAM J. Scientific Computing , 20 , 1998 pages 1-12

with A. Meir and P. Schmidt ,
A two-level discretization method for the stationary MHD equations ETNA
, 6 , 1998 pages 198-210 (http://etna.mcs.kent.edu.)

with V. Ervin
A posteriori error estimation for two level discretizations of flows of electrically conducting incompressible fluids
Computers and Math. w. Appls. , 31 , 1996 pages 105-114

A Posteriori Error estimation and adaptivity

with V. Ervin and J. Maubach
A posteriori error estimation for a two level finite element method for the Navier-Stokes equations
Num. Meth. For P.D.E.'s , 12 , 1996 pages 333-346

with V. Ervin
A posteriori error estimation for two level discretizations of flows of electrically conducting incompressible fluids
Computers and Math. w. Appls. , 31 , 1996 pages 105-114

with V. Ervin and J. Maubach
Adaptive defect correction approach for convection dominated, convection diffusion problems
CTAC95, World Scientific, Computational Techniques and Applications , 1995 pages 1-8

with V. Ervin and J. Maubach
Adaptive defect correction methods for viscous incompressible flow problems ,
SIAM J.N.A. 37[2000]1165-1185.

W. Layton and M. Cawood, V. Ervin and J. Maubach ,
Residual estimators for convection dominated, convection diffusion equations
J. Comp. Applied Math. v.116 , 2000 ,1-22

Variational Multiscale Methods

A connection between subgrid-scale eddy viscosity and mixed methods ,
Applied Math and Computing, 133[2002],147-157.

S. Kaya and W. Layton,
Subgrid scale eddy viscosity is a variational multiscale method,
Preprint, 2002.

W. Layton,
Variational Multiscale Methods annd Subgrid Scale Eddy Viscosity,
in: Computational Fluid Dynamics-Multiscale Methods
(H. Deconinck, editor) ,
Von Karman Institute for Fluid Dynamics,Rhode-Saint-Gen\`ese, Belgium, 2002.

W. Layton,
Model reduction by constraints and an induced pressure stabilization,
J. Numer. Linear Algb. and Applications, 12[2005]547-562.

V John, S Kaya and W Layton,
A two-level variational multiscale method for convection diffusion equations,
Comp. Meth. Appl. Mech. Engrg., 195, 4594-4603, 2006.

Large Eddy Simulation

Solution algorithms for incompressible viscous flows at high Reynolds number
Vestnik Mosk. Gos. Univ. (Computational Math. and Cybernetics)
series , 15 no. 1 , 1996 pages 25-35

A nonlinear subgridscale model for incompressible, viscous flow problems
SIAM J. Sci. Computing , 17 , 1996 pages 347-357

V. John and W. Layton ,
Approximating local averages of fluid velocities: the Stokes problem ,
Computing 66[2001]269-287.

G.P. Galdi and W. Layton,
Approximating the larger eddies in fluid motion II: A model for space filtered flow
Math. Methods and Models in Appl. Sci. v. 10, no. 3 , 2000 pages 1-8

T. Ilieiscu and W. Layton ,
Approximating the larger eddies in fluid motion III: The Boussinesq Model for Turbulent Diffusion,
Analele Stiintifice ale Universitatii ``Al. 1 Cuza'', Series Mathematics, tomul XLIV[1998],245-261.

Approximating the Larger Eddies in Fluid Motion V: A New Scale Similarity Model ,
Mathematical and Computer Modeling 31[2000],1-7.

Analysis of a scale-similarity model of the motion of large eddies in turbulent flows ,
JMAA 264[2001],546-559.

A connection between subgrid-scale eddy viscosity and mixed methods ,
Applied Math and Computing, 133[2002],147-157.

T. Iliescu, V. John, W. Layton, G. Matthies and L. Tobiska,
A numerical study of a class of LES models,
International Journal computational fluid dynamics,17 [2003] 75-85.

V. John and W. Layton,
Analysis of numerical errors in large eddy simulation,
SIAM JNA,40 [2002]995-1020.

T. Iliescu, v. John and W. Layton,
Convergence of finite element approximations of large eddy motion,
Numerical methods for PDE's, 18, 2002, 689-710.

W. Layton,
Bounds on energy dissipation rates of large eddies in turbulent shear flows,
Mathematical and computer modeling, 35, 2002, 1445-1451.

M. Kaya and W. Layton,
On verifiability of models of the motion of large eddies in turbulent flows,
Differential and integrals equations, 15 [2002] 1395-1407.

W. Layton and R. Lewandowski,
Analysis of an eddy viscosity model for large eddy simulation of turbulent flows,
Journal of mathematical fluid mechanics, 2 [2002] 374-399.

A. Dunca, v. John, W. Layton and N. Sahin,
Numerical analysis of large eddy simulation,
359-364 in: DNS/LES progress and challenges
(editors: C. Liu, L. Sakeland and T. Beutner) Greyden press, Columbus, 2001.

A. Dunca, V. John, W.J. Layton,
"The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain",
in G.P. Galdi, J.G. Heywood, R. Rannacher (Eds.),
Contributions to Current Challenges in Mathematical Fluid Mechanics, Advances in Mathematical Fluid Mechanics 3,
Birkhеser Verlag Basel, 53 - 78, 2004

LC. Berselli, G. P. Galdi, T. Iliescu and W. Layton,
Existence of weak solutions for a rational LES model of turbulent flow,
Mathematical methods and models in the applied sciences, 12 (2002), 1131-1152.

V. John, W. Layton and N. Sahin,
Derivation and analysis of near wall models for channel and recirculating flows,
Computers and mathematics with applications,48[2004]1135-1151.

R. Lewandowski and W. Layton,
Un Filtre pour la SGE Etudie a la Lumiere du K41, Journees AUM AFM, 2004.

S. Kaya and W. Layton,
Subgrid scale eddy viscosity is a variational multiscale method,
Preprint, 2002.
W. Layton,
A Mathematical Introduction to Large Eddy Simulation ,
in: Computational Fluid Dynamics-Multiscale Methods
(H. Deconinck, editor) ,
Von Karman Institute for Fluid Dynamics,Rhode-Saint-Gen\`ese, Belgium, 2002.

W. Layton,
Advanced models for large eddy simulation,
in: Computational Fluid Dynamics-Multiscale Methods
(H. Deconinck, editor) , Von Karman Institute for Fluid Dynamics,Rhode-Saint-Gen\`ese, Belgium, 2002.

W. Layton,
Variational Multiscale Methods annd Subgrid Scale Eddy Viscosity,
in: Computational Fluid Dynamics-Multiscale Methods
(H. Deconinck, editor) , Von Karman Institute for Fluid Dynamics,Rhode-Saint-Gen\`ese, Belgium, 2002.

W. Layton and R . Lewandowski,
A simple, accurate and stable scale similarity model for large eddy
simulation: energy balance and existence of weak solutions,
Applied math letters , 16 [2003]1205-1209.

A. Dunca, V. John and W. Layton,
Approximating local averages of fluid velocities: the equilibrium Navier Stokes equations,
Applied numerical mathematics, 49 [2004] 187-205.

M. Anitescu and W. Layton,
Uncertainties in large eddy simulation and improved estimates of turbulent flow functionals,
technical report, 2002, to appear in: SIAM J. Scientiific Computing, 2007.

W. Layton,
Model reduction by constraints and an induced pressure stabilization,
J. Numer. Linear Algb. and Applications, 12[2005]547-562.

M. Anitescu, W. Layton and F. Pahlevani,
Implicit for local effects, explicit for nonlocal is unconditionally stable,
ETNA, , 18[2004]174-187.

S. Kaya, W. Layton and B. Riviere,
Subgrid stabilized defect correction methods for the Navier-Stokes equations ,
SIAM JNA 44 [2006] 1639.

V. John, W Layton and C. Manica,
Time Averaged convergence of algorithms for flow problems,
to appear in: SINUM, (submitted 2005).

W. Layton, C. Manica, M. Neda and L. Rebholz ,
The joint helicity-energy cascade for homogeneous, isotropic
turbulence generated by approximate deconvolution models,
Submitted: Advances and Applications in Fluid Mech., 2007.

W. Layton and R Lewandowski ,
Residual stress of approximate deconvolution models of turbulence,
Journal of Turbulence, 2 [2006] 1-21.

W. Layton and R. Lewandowski,
On a well posed turbulence model,
Discrete and Continuous Dynamical Systems
Series B, Vol 6, nb 1, pp 111-128, 2006

Vincent J. Ervin, W. Layton and Monika Neda,
Numerical Analysis of a Higher Order Time Relaxation Model of Fluids,
Accepted: Inter J Numer Anal & Modeling, 2006.

W. Layton
Bounds on energy and helicity dissipation rates of approximate
deconvolution models of turbulence,
to appear: SIAM J Mathematical Analysis, 2006.

W. Layton, C. Manica, M. Neda and L. Rebholz,
Numerical Analysis and Computational Testing of a high-order Leray-
deconvolution turbulence model,
to appear: Numerical Methods for PDE, 2007.

W. Layton and M. Neda
Truncation of scales by time relaxation
JMAA, 325(2007)788-807.

W. Layton and M. Neda,
A similarity theory of approximate deconvolution models of turbulence,
to appear in: JMAA 2007.

W. Layton and R. Lewandowski
A high accuracy Leray-deconvolution model of turbulence and its
limiting behavior,
to appear: Analysis and Applications, 2007.

W. Layton, A. Labovschii, C. C. Manica, Monika Neda and L. G. Rebholz,
The stabilized, extrapolated trapezoidal-Galerkin finite element method,
submitted to I.J.Comp. and Theoretical Fluid Dynamics: 2007.

W. Layton, I Stanculescu and C. Trenchea,
Theory of the NS-omega model,
technical report, 2007.

A Labovschii, W Layton, C Manica, M Neda, L Rebholz, I Stanculescu and C Trenchea
Mathematical architecture of approximate deconvolution models of turbulence,
technical report, 2007.

W. Layton, C. C. Manica, Monika Neda and L. G. Rebholz,
Numerical analysis of the Navier-Stokes-omega model,
technical report: 2007.

W. Layton, C. C. Manica, Monika Neda, C.D. Pruett and L. G. Rebholz,
TLES: Time filtered Large Eddy Simulation,technical report: 2007.

W Layton and I. Stanculescu,
K41 optimized deconvolution models,
to appear in: Int. J. Computing and Mathematics, 2007.

W Layton and I. Stanculescu,
Chebychev optimized deconvolution models,
in preparation, 2007.

W Layton,
On the accuracy of time relaxation,
technical report, 2007.

Nonlinear PDEs: Analysis and Applications

T. Ilieiscu and W. Layton ,
Approximating the larger eddies in fluid motion III:
The Boussinesq Model for Turbulent Diffusion,
Analele Stiintifice ale Universitatii ``Al. 1 Cuza'',
Series Mathematics, tomul XLIV[1998],245-261.

Approximating the Larger Eddies in Fluid Motion V:
A New Scale Similarity Model ,
Mathematical and Computer Modeling 31[2000],1-7.

Analysis of a scale-similarity model of the motion of large eddies in turbulent flows ,
JMAA 264[2001],546-559.

A. Dunca, V. John, W.J. Layton,
"The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain",
in G.P. Galdi, J.G. Heywood, R. Rannacher (Eds.),
Contributions to Current Challenges in Mathematical Fluid Mechanics, Advances in Mathematical Fluid Mechanics 3,
Birkhеser Verlag Basel, 53 - 78, 2004

LC. Berselli, G. P. Galdi, T. Iliescu and W. Layton,
Existence of weak solutions for a rational LES model of turbulent flow,
Mathematical methods and models in the applied sciences,
12 (2002), 1131-1152.

W. Layton,
Bounds on energy dissipation rates of large eddies in turbulent shear flows,
Mathematical and computer modeling, 35, 2002, 1445-1451.

M. Kaya and W. Layton,
On verifiability of models of the motion of large eddies in turbulent flows,
Differential and integrals equations, 15 [2002] 1395-1407.

W. Layton and R. Lewandowski,
Analysis of an eddy viscosity model for large eddy simulation of turbulent flows,
Journal of mathematical fluid mechanics, 2 [2002] 374-399.

W. Layton and R . Lewandowski,
A simple, accurate and stable scale similarity model for large eddy simulation:
energy balance and existence of weak solutions,
Applied math letters , 16 [2003]1205-1209.

W. Layton and R. Lewandowski,
On a well posed turbulence model,
Discrete and Continuous Dynamical Systems Series B,
Vol 6, nb 1, pp 111-128, 2006

W. Layton
Bounds on energy and helicity dissipation rates
of approximate deconvolution models of turbulence,
to appear: SIAM J Mathematical Analysis, 2006.

W. Layton I Stanculescu and C. Trenchea,
Theory of the NS-omega model,
technical report, 2007.
W. Layton and R. Lewandowski
A high accuracy Leray-deconvolution model of turbulence and its limiting behavior,
to appear: Analysis and Applications, 2007.

Aluminum Reduction Cell Modeling and Simulation

with A. Sunmonu and N.L. Troyani ,
A Mathematical Model of Side-Ledge Position in aluminum reductions cells,
Numer. Methods in Eng. Simulation
(eds: Cerrolaza, Gajardo and Brebbia), Comp. Mech. Publ. Boston , 1996 pages 385-394

N. Troyani, E. Gutierrez and T. Iliescu and W. Layton ,
Corner distribution of voltage in Hall-Heroult aluminum reduction cells ,
Energy Environmental Technological Innovation , 1445-1451 , 1999 .

E. Gutierrez, N. Troyani and T. Iliescu and W. Layton ,
Distribucion de la temperatura en las esquinas de una celda de reduccion de aluminio tipo Hall- Heroult ,
IV Congreso Iberoamericano de Ingenieria Mechanica, Santiago, Chile, 1999.

N Troyani, E Gutierrez and T Iliescu and W. Layton ,
Algoritmos Computacionales para Resolver el Problema Thermoelectrico
en Tres Dimensiones en Celdas de Reduccion de Aluminio del Tipo Hall-Heroult,
Universidad Ciencia y Tecnologia, Vol. 3 , No. 12 [1999] 17-24.

N Troyani, E Gutierrez and T Iliescu and W. Layton ,
Formulacion Variacional del Problema Termoelectrico de una Celda de
Reduccion Hall-Heroult et Tres Dimensiones,
Universidad Ciencia y Tecnologia, Vol. 3 , No. 9 [1999] 25-29.

N Troyani, E Gutierrez and T Iliescu and W. Layton,
The center section temperature distribution in Hall-Heroult aluminum
reduction cells from a three dimensional finite element simulkation,
Proc. Int. Thermal Energy Congress, Izmir, Turkey, 2001.

Graph Theoretic Algorithms and Load Balancing

with V. Ervin and J. Maubach,
Some graph coloring problems in parallel numerical methods
in: Algorithms in de Algebra (A.H. M. Levelt, ed.)
Univ. of Nijmegen, the Netherlands pages 39 48 yr 1993

with R. Jeurissen
Load balancing via graph coloring: an algorithm
Computers Math. Applic. , 27 (No. 3) pages 27-32 , 1994

with V. Ervin
A robust and parallel relaxation method based on algebraic splittings
Numer. Methods for PDE's , 15 , 1999 pages 91-110

Porous media and Coupled Stokes-Darcy flow

W. Layton, F. Schieweck and I. Yotov,
Coupling fluid motion with porous media flow,
SIAM JNA 40 [2002] 2195.

W Layton,
A variational multiscale method for porous media problems and its analysis,
technical report, 2006.

Variational Inequalities

with B. Polman,
Oscillation absorption finite element methods for convection diffusion problems ,
SIAM J.Scientific Computing , 17 , 1996 pages 1328-1346

with J. Maubach and P.J. Rabier ,
Parallel algorithms for maximal monotone operators of local type
Numer. Math. , 71 , 1995 pages 29-58

Linear and Nonlinear elliptic equations

E. Harrell and W. Layton,
Convergence of Finite Element Approximations to Semilinear Elliptic Equations
SIAM J.N.A. , 24 , 1987 pages 52--58

W Layton,
A remark on regularity of an elliptic-elliptic singular perturbation problem,

technical report, 2007.

MHD: Magneto-Hydrodynamics

with W. Lenferink and J. Peterson,
A two-level Newton, finite element algorithm for approximating electrically
conducting, incompressible fluid flows ,
Computers Math. Appls. , 28 yr 1994 pages 21-31

with A. Meir and P. Schmidt ,
A two-level discretization method for the stationary MHD equations
ETNA , 6 , 1998 pages 198-210 (http://etna.mcs.kent.edu.)

with V. Ervin
A posteriori error estimation for two level discretizations of
flows of electrically conducting incompressible fluids
Computers and Math. w. Appls. , 31 , 1996 pages 105-114

Almost Periodic functions

W. Layton,
Existence of Almost Periodic Solutions to Delay Differential
Equations with Lipschitz Nonlinearities
J. Diff. Eqns., 55 , 1984 pages 151--164 , 86d: 34113

L. Drager and W. Layton,
Nonresonance in Functional Differential Equations with Small Time Lag
Proc. Int. Conf. on Func. Diff. Systems and Related Topics III , MR 86f: 43143
W. Layton,
On Nonlinear Difference Approximations to Nonlinear Functional Differential Equations
with L. Drager
Libertas Math. , 3 , 1983 pages 45--65 , MR85j: 34165

L Drager and W. Layton,
Some Results on Nonresonant, Nonlinear Delay Diff. Equations,
Proc. VI Int. Conf. on Trends in Thy. and Prac. of Nonlinear Anal.,
North-Holland Publishing Co. , 1984 pages 131-136

W. Layton,
The Galerkin Method for the Approximation of Almost Periodic Solutions of Functional Differential Equations
Funk. Eva. , 29 , 1986 pages 19--29

Education in Computational Science and Engineering

W Layton and R. Roskies,
Teaching Physicists How to Program ,
Computers in Physics , 2 , 1988 pages 22--27

Nonlinear Delay Eequations:

Periodic Solutions of Nonlinear Delay Equations ,
Jour. Math. Anal. and Appl , 77 , 1980 pages 198--204 , MR 982a: 34093

W. Layton,
On the Existence of Periodic Solutions of x'' (t) + g(x(t), x(t - tau)) = B(x) ,
Nonlinear Analysis , 6 yr 1982 pages 863--872 , MR 83m: 34072

L. Drager and W. Layton,
Non-linear Delay Differential Equations and Function Algebras ,
in: Proc. Int. Conf. on Diff. Eqns.
eds I. Knowles and R. Lewis , North-Holland Publishing Co., 1983 pages 149--154 , MR 86i: 34089

W. Layton,
Existence of Almost Periodic Solutions to Delay Differential Equations with Lipschitz Nonlinearities
J. Diff. Eqns., 55 , 1984 pages 151--164 , 86d: 34113

L. Drager and W. Layton,
Nonresonance in Functional Differential Equations with Small Time Lag
Proc. Int. Conf. on Func. Diff. Systems and Related Topics III , MR 86f: 43143

L Drager and W. Layton,
On Nonlinear Difference Approximations to Nonlinear Functional Differential ,
Libertas Math. , 3 , 1983 pages 45--65 , MR85j: 34165

with L. Drager
Bounded solutions of delay differential equations subject to a generalized nonresonance condition
J.D.E. , 131 , 1996 pages 132-169

with L. Drager
Initial value problems in nonlinear, nonresonant delay differential equations with possibly infinite delay
EJDE, no. 24 , 1997 , 1997 pages 1-20