Applications of Mathematics

, Volume 62, Issue 4, pp 297–317

Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition

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Abstract

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.

Keywords

method of fundamental solutions biharmonic equation Almansi-type decomposition 

MSC 2010

65N80 31A30 49M27 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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