A high order finite volume element method for solving elliptic partial integro-differential equations

摘要

In this paper, we develop a finite volume element method of order p for solving elliptic integro-differential equations in two dimensions. These types of equations arise in questions of hereditary phenomena in physics. The H~1 norm error estimates are discussed, the convergence result in H~1 norm is proved and some numerical results are studied to illustrate the effectiveness of the method.