Ewing, R. E. and T. F. Russell, “Multistep Galerkin Methods along Characteristics for Convection-Diffusion Problems,” In: R. Vichnevetsky and R. S. Stepkman, Eds., Advances in Computer Methods for Partial Differential Equations, IMACS, Rutgers University, New Brunswick, 1981, pp. 28-36.

has been cited by the following article:

• 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.