Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Provides a numerical method for solving space fractional diffusion equations on irregular convex domains, addressing a computational bottleneck in fractional PDEs.
Developed a Galerkin finite element method for 2D Riesz space fractional diffusion equations with nonlinear source terms on convex domains, enabling stiffness matrix formation on unstructured triangular meshes. Numerical examples verified accuracy and stability.
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.