  In this paper, we consider two-dimensional Riesz space fractional diffusion
equations with nonlinear source term on convex domains. Applying Galerkin
finite element method in space and backward difference method in time, we
present a fully discrete scheme to solve Riesz space fractional diffusion
equations. Our breakthrough is developing an algorithm to form stiffness matrix
on unstructured triangular meshes, which can help us to deal with space
fractional terms on any convex domain. The stability and convergence of the
scheme are also discussed. Numerical examples are given to verify accuracy and
stability of our scheme.
