Optimal Convergence Analysis for Convection Dominated Diffusion Problems

M. A. Mohamed Ali

Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt.

DOI: 10.4236/jamp.2013.13004                

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 two-step Euler backward difference scheme.

Keywords

H¹-Galerkin Mixed Finite Element Method; Characteristics Method; LBB Condition; Optimal Error Estimates; and Euler Backward Difference Scheme

Conflicts of Interest

The authors declare no conflicts of interest.

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