The boundary element spline collocation for nonuniform meshes on the torus
The paper is concerned with the boundary element spline collocation method on the torus for a class of strongly elliptic biperiodic pseudodifferential equations. This class includes the single layer and hypersingular operators. As trial functions tensor products of odd degree splines are used and the collocation is imposed at the nodal points of the tensor product mesh. The analysis of the method is based on a variant of the Arnold-Wendland Lemma. It is shown that if the maximum mesh length is small enough, the collocation problem has a unique solution. Moreover, the approximation is stable and quasioptimal with respect to a norm depending on the order of the operator and the degree of the splines. Asymptotic convergence results are given for general and quasiuniform meshes.
strongly elliptic pseudodifferential operators
scientific article; zbMATH DE number 5151304