TITLE:
Optimal Convergence Analysis for Convection Dominated Diffusion Problems
AUTHORS:
M. A. Mohamed Ali
KEYWORDS:
H1-Galerkin Mixed Finite Element Method; Characteristics Method; LBB Condition; Optimal Error Estimates; and Euler Backward Difference Scheme
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.3,
September
20,
2013
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.