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

作者：Wang, Hong; Yang, Danping; Zhu, Shengfeng^*

来源：Computer Methods in Applied Mechanics and Engineering, 2015, 290: 45-56.

DOI：10.1016/j.cma.2015.02.027

• Discontinuous Petrov-Galerkin framework
• Fractional diffusion equations
• Petrov-Galerkin finite element method
• Weak coercivity

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.
We utilize the discontinuous Petrov-Galerkin (DPG) framework to develop a Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations. We prove the well-posedness and optimal-order convergence of the Petrov-Galerkin finite element method. Numerical examples are presented to verify the theoretical results.

• 出版日期2015-6-15
• 单位华东师范大学