Discontinuous piecewise polynomial collocation in two dimensions

Abstract

We consider collocation method based on a piecewise polynomial approach in two spatial dimensions. Our model uses a finite element partition where the interpolation may be discontinuous across element boundaries. The underlying topological structure is the continuous or bounded functions with sup-norm. To ensure broad applicability we use a triangular finite element partition. We include a convergence result and examples. The examples include comparisons to finite element method and examples from finance.