Note:  Address for correspondence: John Loustau, Hunter College, New York, NY 10065, USA. E-mail: [email protected]
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.
Keywords: Collocation method, finite element method, piecewise polynomial interpolation, triangulation