WIT Press


Cauchy Problem For The Biharmonic Equation Solved Using The Regularization Method

Price

Free (open access)

Paper DOI

10.2495/EBEM980271

Volume

20

Pages

10

Published

1998

Size

731 kb

Author(s)

A. Zeb, L. Elliott, D.B. Ingham & D. Lesnic

Abstract

The boundary element method (BEM) is applied to discretise numerically a Cauchy problem for the biharmonic equation which involves over- and under- specified boundary portions of the solution domain. The resulting ill-conditioned system of linear equations is solved using the regularization method. It is shown that the regularization method performs better than the minimal energy method in the case of the biharmonic equation, unlike the Laplace equation where the minimal energy method is more efficient. Moreover, the stability of the numerical solution obtained by the regularization method is also investigated. 1 Introduction Perhaps the most classical example of an ill-posed problem is that of the Cauchy problem for the Laplace equation and some references dealing with

Keywords