The Residual-Free-Bubble Finite Element Method on Anisotropic Partitions.

Journal article

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 Qk., k ≥ 1. In the case of P1 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. © 2007 Society for Industrial and Applied Mathematics.

Authors: Cangiani, A; Süli, E

• Publication status: Published
• Journal: SIAM J. Numerical Analysis
• Volume: 45
• Issue: 4
• Pages: 1654-1678
• Publication date: 2007-01-01
• DOI: 10.1137/060658011
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: stabilized finite element methods; residual-free-bubble finite element method; convection-dominated diffusion problems