Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8053992 | Applied Mathematics Letters | 2018 | 10 Pages |
Abstract
The inverse Cauchy problem of Laplace equation is hard to solve numerically, since it is highly ill-posed in the Hadamard sense. With this in mind, we propose a natural regularization technique to overcome the difficulty. In the linear space of the Trefftz bases for solving the Laplace equation, we introduce a novel concept to construct the Trefftz energy bases used in the numerical solution for the inverse Cauchy problem of the Laplace equation in arbitrary star plane domain. The Trefftz energy bases not only satisfy the Laplace equation but also preserve the energy, whose performance is better than the original Trefftz bases. We test the new method by two numerical examples.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Chein-Shan Liu, Fajie Wang, Yan Gu,