The research is in the general fields of numerical analysis, applied partial differential equations and scientific computing. Most work is on the numerical approximation of partial differential equations. The most significant contributions are in absorbing boundary conditions of computational boundaries, high resolution algorithms for nonlinear hyperbolic conservation laws and convergence theory for approximations of oscillatory solutions to partial differential equations. Other fields of research is homogenization theory for nonlineal differential equations, approximation of differential algebraic equations and wavelet approximation methods for evolution equations.
Applications are mainly to problems from fluid mechanics and electro-magnetics.