An Error Estimates for Convection Dominated Diffusion Problems

Abstract

In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1- Galerkin mixed finite element method avoids completely the imposition of such a condition on the approximating spaces. In this article, we discuss and analyze error estimates for Convection- dominated diffusion problems using H1-Galerkin mixed finite element method, along with the method of characteristics. Optimal order of convergence has been achieved for the error estimates of a single-step Euler backward difference scheme. Keywords. H1- Galerkin mixed finite element method, Characteristics method, LBB condition, optimal error estimates, and Euler backward difference scheme.