The Residual-Free-Bubble Finite Element Method on Anisotropic Partitions
Abstract
The subject of this work is the analysis and implementation of stabilized finite element methods on anisotropic meshes. We develop the anisotropic a priori error analysis of the residual-free-bubble (RFB) method applied to elliptic convection-dominated convection-diffusion problems in two dimensions, with finite element spaces of type $Q_k$, $k \geq 1$. In the case of $P_1$ finite elements, relying on the equivalence of the RFB method to classical stabilized finite element methods, we propose a new rule, justified through the analysis of the RFB method, for selecting the stabilization parameter in classical stabilized methods on two-dimensional anisotropic triangulations.
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Copyright © 2007 Society for Industrial and Applied Mathematics.
History
Submitted: 24 April 2006
Accepted: 9 May 2007
Published online: 17 August 2007
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