Our interests continue to evolve and expand. Here is a selection of some of our current interests:

• Numerical Optimization, Constrained Optimization, Differential Algebraic Equation, Applications
• Computational Fluid Dynamics, Large Eddy Simulation and Turbulence More on LES , Finite Element Methods for Fluid Flow and Natural Convection Problems, Parallel Algorithms for Nonsymmetric Problems, Multi-scale Discretizations of Flow Problems, Uncertainties in Turbulent Flow Simulations.
• Numerical analysis of flow and transport processes in porous media, Large scale scientific computing with applications to flow in porous media, Massively parallel simulations of multiphase porous media and surface flows on irregular multiblock domains, High-order discretizations of single phase and multiphase flow in fractured and heterogeneous porous medium, Numerical modeling of miscible displacement for stable and unstable flows, Multinumerics approaches (coupling of discontinuous Galerkin and mixed finite element methods for single phase flow), Multiphysics approaches (coupling of Stokes and Darcy flows using a discontinuous Galerkin method), Multi-numerics/multi-physics approaches (coupling of classical finite element and mixed finite element methods for the coupled Stokes/Darcy problem, coupling of discontinuous Galerkin and mixed finite element methods for the coupled Stokes/Darcy problem).
• Finite Element Methods Discontinuous Galerkin finite element methods, numerical analysis of partial differential equations, Domain Decomposition, Adaptivity, Mixed Finite Element (MFE) Methods, FEM's for Hyperbolic Systems and Elliptic-Hyperbolic Singular Perturbation Problems design and analysis of accurate discretization techniques (mixed finite elements, finite volumes, finite differences)
• Large Scale Scientific Computing Efficient nonlinear iterative solvers (domain decomposition, multigrid, Newton-Krylov methods), Multi-numerics Approach: Theoretical Error Analysis , Multi-physics Approach: Theoretical Error Analysis, Multi-Level Newton Methods, Numerical Linear Algebra, Adaptive and parallel algorithms.
• Analysis A priori and a posteriori error analysis, Well-posedness of nonlinear models, Functional analysis, Nonlinear analysis applied to ordinary differential equations and partial differential equations.
• Applications, Modeling and simulation of aluminum reduction cells, Applications of Porous Media Modeling and Simulation, Uncertainty sensitivity and design in CFD applications, Turbulence Modeling, Modeling of seismic waves in heterogeneous media, Modeling of viscoelastic solids, Parallel computing.