New boundary element formulas for the biharmonic equation
The paper is devoted to the Dirichlet problem of the biharmonic equation on a plane domain with a smooth boundary. The author proposes two new boundary integral equation formulas for this problem. The formulas are based on a new fundamental solution that is dependent on the domain. This method leads to scalar integral equations instead of a non-symmetric matrix system of integral equations. The ellipticity and solvability of these new formulas are studied. Numerical experiments for simple Galerkin methods are also provided.
scientific article; zbMATH DE number 1279277