Convergence of a finite volume element method for a generalized Black-Scholes equation transformed on finite interval

摘要

In this paper we present a convergence analysis of a positivity-preserving fitted finite volume element method (FVEM) for a generalized Black-Scholes equation transformed on finite interval, degenerating on both boundary points. We first formulate the FVEM as a Petrov-Galerkin finite element method using a spatial discretization, previously proposed by the author. The Garding coercivity of the corresponding discrete bilinear form is established. We obtain stability and error bounds for the solution of the fully-discrete system. Analysis of the impact of the finite domain transformation on the numerical solution of the original problem is given.