Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems
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.
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.
[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.
Published
2023-01-26
Issue
pp. 661- 675
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Uściłowska-Gajda, A., Kołodziej, J. . A., Ciałkowski, M., & Frąckowiak, A. (2023). Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems. Computer Assisted Methods in Engineering and Science, 10(4), 661-675. https://cames3.ippt.pan.pl/index.php/cames/article/view/1073
