In these notes, we study the Runge Kutta Discontinuous Galerkin method for numericaly
solving nonlinear hyperbolic systems and its extension for convection-dominated problems …

An unwelcome feature of the popular streamline upwind/Petrov–Galerkin (SUPG)
stabilization of convection-dominated convection–diffusion equations is the presence of …

This is the second paper in a series in which we construct and analyze a class of TVB (total
variation bounded) discontinuous Galerkin finite element methods for solving conservation …

In this paper we study the two-dimensional version of the Runge-Kutta Local Projection
Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one …

In recent years there have been significant developments in the development of stable and
accurate finite element procedures for the numerical approximation of a wide range of fluid …

Galerkin/least-squares finite element methods are presented for advective-diffusive
equations. Galerkin/least-squares represents a conceptual simplification of SUPG, and is in …

We study the entropy stability of difference approximations to nonlinear hyperbolic
conservation laws, and related time-dependent problems governed by additional dissipative …

Some stabilized finite element methods for the Stokes problem are reviewed. The Douglas-
Wang approach confirms better stability features for high order interpolations. Next, the …

A space-time element method is presented for solving the compressible Euler and Navier-
Stokes equations. The proposed formulation includes the variational equation, predictor …

We present multicomponent flow models derived from the kinetic theory of gases and
investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial …