Fluid Mechanics

• A nonconforming finite element method for the stationary Navier-Stokes equations.
• Numerical simulation of incompressible fluid flow using locally solenoidal elements.
• Stability of solitary-wave solutions of systems of dispersive equations

Discontinuous Galerkin Methods

•  Two-level non-overlapping additive Schwarz method for a discontinuous Galerkin method
•  A-posteriori error estimates for a discontinuous Galerkin approximation of second order elliptic problems
•  Adaptive discontinuous Galerkin approximations of second-order elliptic problems
•  Two-level non-overlapping additive Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation
•  Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic equations
•  Conservative discontinuous-Galerkin methods for the Genralized Korteweg-de Vries equation
•  A posteriori error estimates for discontinuous Galerkin methods for the Generalized Korteweg-de Vries equation
•  A posteriori error estimates of conservative local discontinuous Galerkin methods for the Generalized Korteweg-de Vries equation
•  Two-level additive Schwarz methods for discontinuous Galerkin approximations of second order elliptic equations
•  Two-level additive Schwarz methods for discontinuous Galerkin approximations of the biharmonic equation

Cahn_Hilliard

•  Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition
•  A mixed discontinuous Galerkin, convex-splitting scheme for a modified Cahn-Hilliard equation and an efficient Multigrid solver
•  Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn-Hilliard equation with a mass source

Finite Time Blow-Up for NLS

•  Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrodinger equation.

Space-time finite element methods

•  A Space-time finite element method for the nonlinear Schr\"odinger equation: The discontinuous Galerkin method.
•  A Space-time finite element method for the nonlinear Schr\"odinger equation: The continuous Galerkin method.
•  Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations.