Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes. (8th January 2008)

• Record Type: Journal Article
• Authors: Stynes, Martin
• Is Part Of: International journal of computing science and mathematics. Volume 1:Number 2/3/4(2007)
• Page Start: 412
• Page End: 431
• Publication Date: 2008-01-08
• Subjects: convection-diffusion -- boundary layers -- interior layers -- Shishkin meshes -- SDFEM -- SUPG -- streamline diffusion FEM -- finite element method; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.