Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D. Quasi-optimal convergence rate for an adaptive boundary element method. (English) Zbl 1273.65186 SIAM J. Numer. Anal. 51, No. 2, 1327-1348 (2013). The authors are concerned with the lowest-order Galerkin boundary element method (BEM) in order to solve the weakly singular intergral equation associated with the simple layer potential of 3D Laplacian. They introduce an \(h\)-adaptive BEM in the following steps: solve, estimate, mark and refine. They also show its linear convergence and identify an approximation class for which the method converges at the optimal rate. The adaptive technique is illustrated on the 2D screen problem known for strong edge singularities of its solution. Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) Cited in 37 Documents MSC: 65N38 Boundary element methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:adaptive boundary element method; adaptive algorithm; error reduction; optimal convergence; screen problem; Laplace equation; numerical examples; Galerkin boundary element method; weakly singular intergral equation; simple layer potential PDFBibTeX XMLCite \textit{M. Feischl} et al., SIAM J. Numer. Anal. 51, No. 2, 1327--1348 (2013; Zbl 1273.65186) Full Text: DOI Link