Name
Abstract | ||
|---|---|---|
It is well known that the regularity of solutions of elliptic partial differential equations on domains with re-entrant corners is limited by the maximal interior angle. This results in reduced convergence rates for finite element approximations on families of quasi-uniform meshes. Following an idea of Zenger and Gietl, we show that it is possible to regain the full order of convergence by a local modification of the bilinear form in a vicinity of the singularity and thus to overcome the pollution effect. A complete convergence analysis in weighted Sobolev spaces is presented, and we also show that the stress intensity factors can be computed with optimal accuracy. The theoretical results are illustrated by numerical tests that demonstrate second order convergence of linear finite elements on families of quasi-uniform meshes. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/120871377 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
corner singularities,pollution effect,finite element methods,optimal convergence rates,stress intensity factors,weighted Sobolev spaces | Mathematical optimization,Normal convergence,Mathematical analysis,Compact convergence,Extended finite element method,Finite element method,Rate of convergence,Elliptic partial differential equation,Mathematics,hp-FEM,Modes of convergence | Journal |
Volume | Issue | ISSN |
52 | 1 | 0036-1429 |
Citations | PageRank | References |
4 | 0.47 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Herbert Egger | 1 | 45 | 11.44 |
| Ulrich Rüde | 2 | 505 | 72.00 |
| Barbara I. Wohlmuth | 3 | 320 | 50.97 |