Title: Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes

Authors: Martin Stynes

Addresses: Mathematics Department, National University of Ireland, Cork, Ireland

Abstract: First, a brief description of linear convection-diffusion-reaction problems is given. Then the Streamline Diffusion Finite Element Method (SDFEM, also known as SUPG) is introduced. Since its inception in 1979, this method has been the subject of a huge number of theoretical analyses and numerical investigations. The body of this survey paper is a comprehensive overview of what is known about the method where its strengths and weaknesses are discussed and recent theoretical results are included; in particular, Shishkin meshes are introduced and the behaviour of the SDFEM on these meshes is discussed.

Keywords: convection-diffusion; boundary layers; interior layers; Shishkin meshes; SDFEM; SUPG; streamline diffusion FEM; finite element method.

DOI: 10.1504/IJCSM.2007.016543

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.412 - 431

Published online: 07 Jan 2008 *

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