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

Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains