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Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition. (English) Zbl 1488.65722

Summary: The aim of this paper is to analyze mathematically the method of fundamental solutions applied to the biharmonic problem. The key idea is to use Almansi-type decomposition of biharmonic functions, which enables us to represent the biharmonic function in terms of two harmonic functions. Based on this decomposition, we prove that an approximate solution exists uniquely and that the approximation error decays exponentially with respect to the number of the singular points. We finally present results of numerical experiments, which verify the sharpness of our error estimate.

MSC:

65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
49M27 Decomposition methods
65N15 Error bounds for boundary value problems involving PDEs
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