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IMA Journal of Numerical Analysis 2001 21(1):53-80; doi:10.1093/imanum/21.1.53
© 2001 by Institute of Mathematics and its Applications
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Exponential convergence in a Galerkin least squares hp-FEM for Stokes flow

Dominik Schötzau1 and Christoph Schwab2

1 School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, MN 55455, USA, e-mail: schoetza{at}math.umn.edu 2 Seminar für Angewandte Mathematik, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland, e-mail: schwab{at}sam.math.ethz.ch

A stabilized hp-finite element method (FEM) of Galerkin least squares (GLS) type is analysed for the Stokes equations in polygonal domains. Contrary to the standard Galerkin FEM, the GLSFEM admits the implementationally attractive equal-order interpolation in the velocity and the pressure. In conjunction with geometrically refined meshes and linearly increasing approximation orders it is shown that the hp-GLSFEM leads to exponential rates of convergence for solutions exhibiting singularities near corners. To obtain this result a novel hp-interpolation result is proved that allows the approximation of pressure functions in certain weighted Sobolev spaces in a conforming way and at exponential rates of convergence on geometric meshes.

Received 6 June 1999. Accepted 14 March 2000.


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