A fast finite volume method for conservative space–time fractional diffusion equations discretized on space–time locally refined meshes

Abstract

A fast finite volume method was developed for conservative space–time fractional diffusion partial differential equations in two space dimensions. In the method a locally refined composite spatial mesh is used to resolve the boundary layers of the solutions and a graded temporal mesh is used to resolve the singularity of the solutions near the initial time. A fast numerical method was developed by fully exploring the structure of the stiffness matrices. Numerical results show the utility of the method.