A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem

This paper reports a new boundary-integral-equation method (BIEM) for numerically solving biharmonic problems with Dirichlet boundary conditions. For the solution of these problems in convex polygons, it was found that the accuracy of the conventional BIEM is significantly reduced, and spurious oscillatory behaviour is often observed in the boundary solutions especially for areas near corners (Mai-Duy N, Tanner RI. An effective high order interpolation scheme in BIEM for biharmonic boundary value problems. Eng Anal Bound Elem 2005;29:210–23). In this study, a new treatment for these difficulties is proposed. The unknown functions in boundary integrals are approximated using a domain-type interpolation scheme rather than traditional boundary-type interpolation schemes. Two test problems are considered to validate the formulation and to demonstrate the attractiveness of the proposed method.