Name
Abstract | ||
|---|---|---|
For the simple layer potential V associated with the three-dimensional (3D) Laplacian, we consider the weakly singular integral equation V phi = f. This equation is discretized by the lowest-order Galerkin boundary element method. We prove convergence of an h-adaptive algorithm that is driven by a weighted residual error estimator. Moreover, we identify the approximation class for which the adaptive algorithm converges quasi-optimally with respect to the number of elements. In particular, we prove that adaptive mesh refinement is superior to uniform mesh refinement. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/110842569 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
adaptive boundary element method,adaptive algorithm,error reduction,optimal convergence | Mathematical optimization,Mathematical analysis,Galerkin method,Adaptive mesh refinement,Boundary element method,Rate of convergence,Adaptive algorithm,Method of mean weighted residuals,Mathematics,Laplace operator,Estimator | Journal |
Volume | Issue | ISSN |
51 | 2 | 0036-1429 |
Citations | PageRank | References |
10 | 0.66 | 16 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M Feischl | 1 | 52 | 7.67 |
| Michael Karkulik | 2 | 47 | 6.50 |
| Jens Markus Melenk | 3 | 133 | 24.18 |
| Dirk Praetorius | 4 | 121 | 22.50 |