ADAPTIVE APPROXIMATIONS FOR 3-D ELECTROSTATIC PLATE PROBLEMS

The solution of a weakly singular integral equation on a plane surface piece GAMMA is approximated via the Galerkin method, using piecewise constant elements. The determination of the solution of this integral equation (with the single layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate GAMMA loaded with a given potential. The capacitance of GAMMA is proportional to the integral of the charge density, Within, two adaptive strategies are presented, which based upon an approximation of the local residue, refine the grid locally. Numerical results are given for the unknown capacitance which indicate an exponential rate of convergence of the boundary element Galerkin method.