Exponential convergence in a Galerkin least squares hp-FEM for Stokes flow |
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Authors: | Schotzau, Dominik Schwab, Christoph |
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Affiliation: | 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 |
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Abstract: | A stabilized hp-finite element method (FEM) of Galerkin leastsquares (GLS) type is analysed for the Stokes equations in polygonaldomains. Contrary to the standard Galerkin FEM, the GLSFEM admitsthe implementationally attractive equal-order interpolationin the velocity and the pressure. In conjunction with geometricallyrefined meshes and linearly increasing approximation ordersit is shown that the hp-GLSFEM leads to exponential rates ofconvergence for solutions exhibiting singularities near corners.To obtain this result a novel hp-interpolation result is provedthat allows the approximation of pressure functions in certainweighted Sobolev spaces in a conforming way and at exponentialrates of convergence on geometric meshes. Received 6 June 1999. Accepted 14 March 2000. |
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