Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems

A. Uściłowska-Gajda; J . A. Kołodziej; M. Ciałkowski; A. Frąckowiak

A. Uściłowska-Gajda Poznań University of Technology
J . A. Kołodziej Poznań University of Technology
M. Ciałkowski Poznań University of Technology
A. Frąckowiak Poznań University of Technology

Abstract

The solution of inhomogeneous elliptic problems by the Trefftz method has become increasingly more popular during the last decade [1- 3]. One method of solution uses the fundamental solutions as trial functions and the inhomogeneous part is expressed by radial basis functions (RBFs). The purpose of this paper is to solve several boundary value problems that have exact solutions. Two error criteria are used for comparison of the exact solutions and the approximated solutions. The first is the mean least square global error. The second has a local character, as it measures the absolute maximal error.

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References

[1] V. M. A. Leitao. A meshless method for Kirchoff plate bending problems. Int. J. Num. Meth. Engrg., 52: 1107- 1130, 2001
[2] A. Poillikkas, A. Karageorghis, and G. Georgiou. The method of fundamental solutions for inhomogeneous elliptic problems. Computational Mechanics, 22: 100-107, 1998.
[3] P. A. Ramachandran, K. Balakrishnan. Radial basis functions as approximate particular solutions: Review of recent progress. Eng. Anal. Bound. Elem., 24: 575-582, 2000.
[4] M. Ciałkowski, A. Frąckowiak. Heat functions and their applications to solving the heat conduction and the mechanical problems (in Polish). Publishing House of Poznań University of Technology, 2000.