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Quasi-optimal convergence rate for an adaptive boundary element method. (English) Zbl 1273.65186

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.

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
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