Uniform convergence of an upwind finite element method on layer-adapted grids

✍ Scribed by Dyrk Schneider; Hans-Görg Roos; Torsten Linß

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 136 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(00)00328-5

✦ Synopsis

A singularly perturbed convection±diusion problem is considered. The problem is discretised using an upwinded ®nite element method on layer-adapted meshes. We establish convergence of almost ®rst-order in a weighted energy norm, no matter how small the perturbation parameter. As a corollary we derive bounds for the maximum-norm error. Numerical experiments support the theoretical results.