A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations

摘要

Fractional diffusion equations have found increasingly more applications in recent years but introduce new mathematical and numerical difficulties. Galerkin formulation, which was proved to be coercive and well-posed for fractional diffusion equations with a constant diffusivity coefficient, may lose its coercivity for variable-coefficient problems. The corresponding finite element method fails to converge.