Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
作者：
Highlights：
• A locally-conservative expanded mixed finite element scheme is developed based on the saddle-point variational formulation.
• The well-posedness of the saddle-point variational formulation and the expanded mixed formulation is established.
• The equivalence of the negative fractional spaces and the negative Sobolev spaces is established.
• Optimal order error estimates are derived for sufficiently smooth solution and non-smooth solution.
摘要
•A locally-conservative expanded mixed finite element scheme is developed based on the saddle-point variational formulation.•The well-posedness of the saddle-point variational formulation and the expanded mixed formulation is established.•The equivalence of the negative fractional spaces and the negative Sobolev spaces is established.•Optimal order error estimates are derived for sufficiently smooth solution and non-smooth solution.
论文关键词：Conservative fractional diffusion equation,Saddle-point variational formulation,Well-posedness,Expanded mixed finite element method,Optimal-order error analysis,Numerical experiments
论文评审过程：Received 18 October 2014, Revised 8 June 2015, Available online 24 October 2015, Version of Record 11 November 2015.
论文官网地址：https://doi.org/10.1016/j.cam.2015.09.022
