Using rectangular Qp elements in the SDFEM for a convection--diffusion problem with a boundary layer

Authors:
Martin Stynes;Lutz Tobiska
Affiliations:
National University of Ireland, Cork, Ireland;Institut für Analysis und Numerik, Otto-von-Guericke Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

The streamline diffusion finite element method (SDFEM; the method is also known as SUPG) is applied to a convection-diffusion problem posed on the unit square whose solution has exponential boundary layers. A rectangular Shishkin mesh is used. The trial functions in the SDFEM are piecewise polynomials that lie in the space Q"p, i.e., are tensor products of polynomials of degree p in one variable, where p1. The error bound @?I"Nu-u^N@?"S"D=