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Theoretical and numerical study of a free boundary problem by boundary integral methods. (English) Zbl 0985.35114
Summary: We study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in an equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

MSC:
35R35 Free boundary problems for PDEs
31A10 Integral representations, integral operators, integral equations methods in two dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
42A10 Trigonometric approximation
45G05 Singular nonlinear integral equations
65R20 Numerical methods for integral equations
41A15 Spline approximation
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