Discontinuous piecewise polynomial collocation in two dimensions

Issue title: Financial Derivatives and Risk Models

Article type: Research Article

Authors: Loustau, John^; | Irwin, Scott | Lindorff, Ariel | Svadlenka, John

Affiliations: Hunter College, New York, NY, USA

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

DOI: 10.3233/RDA-2012-0076

Journal: Risk and Decision Analysis, vol. 4, no. 1, pp. 47-57, 2013