Name
Title | ||
|---|---|---|
Simple a posteriori error estimators for the h-version of the boundary element method |
Abstract | ||
|---|---|---|
The h-h/2-strategy is one well-known technique for the a posteriori error estimation for Galerkin discretizations of energy minimization problems. One considers to estimate the error , where is a Galerkin solution with respect to a mesh and is a Galerkin solution with respect to the mesh obtained from a uniform refinement of . This error estimator is always efficient and observed to be also reliable in practice. However, for boundary element methods, the energy norm is non-local and thus the error estimator η does not provide information for a local mesh-refinement. We consider Symm’s integral equation of the first kind, where the energy space is the negative-order Sobolev space . Recent localization techniques allow to replace the energy norm in this case by some weighted L 2-norm. Then, this very basic error estimation strategy is also applicable to steer an h-adaptive algorithm. Numerical experiments in 2D and 3D show that the proposed method works well in practice. A short conclusion is concerned with other integral equations, e.g., the hypersingular case with energy space , respectively, or a transmission problem. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/s00607-008-0017-4 | Computing |
Keywords | Field | DocType |
integral equation,energy minimization,boundary element method,exact solution | Mathematical optimization,Mathematical analysis,Galerkin method,Sobolev space,A priori and a posteriori,Integral equation,Boundary element method,Adaptive algorithm,Mathematics,Energy minimization,Estimator | Journal |
Volume | Issue | ISSN |
83 | 4 | 0010-485X |
Citations | PageRank | References |
5 | 0.61 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Ferraz-Leite | 1 | 6 | 1.34 |
| Dirk Praetorius | 2 | 121 | 22.50 |