Adaptive approximations for 3-D electrostatic plate problems
The charge density of a thin, electrified plate \(\Gamma\) loaded with a given potential is determined as the solution of a weakly singular integral equation. An approximate solution is found by the Galerkin scheme in a subspace of certain Sobolev spaces of distributions on \(\Gamma\). The space of piecewise constant functions of a grid of \(\Gamma\) is used, and the capacitance of the plate \(\Gamma\) is computed from the approximated charge density. In order to increase the convergence rate an adaptive method for the grid refinement is applied and two strategies are presented. The two refinement strategies are illustrated on two examples, where the domain is either a parallelogram or an \(L\)-shaped region.
scientific article; zbMATH DE number 221755