Cauchy Problem For The Biharmonic Equation
Solved Using The Regularization Method
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
Related Book
Other papers in this volume
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