Multi-level biharmonic and bi-Helmholtz interpolation with application to the boundary element method
The interpolation problem reformulated in variational form is applied to the biharmonic and the bi-Helmholtz equations. Existence and uniqueness of the solution are proved in Sobolev spaces. The approximation properties of this interpolation are investigated. A multi-level method is presented which is based on a quadtree/octtree cell system generated by the interpolation points. Some applications to solving partial differential equations are outlined.
scientific article; zbMATH DE number 1559248