We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...

We describe a shock-capturing streamline diffusion space-time discontinuous Galerkin (DG) method to discretize the shallow water equations with variable bottom topography. This method, based on the entropy variables as degrees of freedom, is shown to be energy stable as well as well-balanced with respect to the lake at rest steady state. We present numerical experiments illustrating the numeric...

This paper aims to give the reader a summary of current understanding of the streamlinediffusion finite element method (SDFEM), as applied to linear steady-state convection-diffusion problems. Towards this end, we begin with a brief description of the nature of convectiondiffusion problems: the structure of their solutions will be examined, with special emphasis on the main phenomena of exponen...

We present and analyze extensions of the streamline diffusion finite element method to the time-dependent two-dimensional Navier-Stokes equations for an incompressible fluid in the case of high Reynolds numbers. The limit case with zero viscosity, the Euler equations, is also considered. Introduction. The Streamline Diffusion method is a finite element method for convection-dominated convection...

The purpose of the paper is to introduce a novel cell boundary element (CBE) method for the convection dominated diffusion equation. The CBE method can be viewed as a Petrov-Galerkin type method defined on the skeleton of a mesh. The proposed method utilizes continuity of normal flux on each inter-element boundary. By constructing a local basis (mesh-oriented element) that is dependent upon the...

We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit tim...

This article presents a study on singularly perturbed 1D parabolic Dirichlet’s type differential equations with discontinuous source terms an interior line. The time derivative is discretized using the Euler backward method, followed by application of streamline–diffusion finite element method (SDFEM) to solve locally one-dimensional stationary problems Shishkin mesh. Our proposed shown achieve...