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J. Douglas Jr., R. E. Ewing and M. F. Wheeler, “A Time-Discretization Procedure for a Mixed Finite Element Approximation of Miscible Displacement in Porous Media,” ESAIM: Mathematical Modelling and Numerical Analysis: Modélisation Mathématique et Analyse Numérique, Vol. 17, No. 3, 1983, pp. 249-265.

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.