A h-Version of the Least Squares Collocation Method for the Biharmonic Equation in Irregular Domains

Abstract

The numerical solution of boundary value problems for the biharmonic equation in irregular domains was obtained by new h-versions of the high-order accuracy least squares collocation method. In particular, we consider discrete boundary and multiply connected domains. It is shown that our approximate solution is high order accurate. We represent some suitable numerical examples. The numerical results are compared with those found by other authors who used a high order finite difference method. The biharmonic equation was applied to model the stress-strain state of isotropic thin irregular plates in the theory of thin plates.