Solvability and approximation of two-side conservative fractional diffusion problems with variable-Coefficient based on least-Squares

作者：

Highlights：

• Prove that two-side fractional operator is surjective from solution space to L2.

• Solution space is a sum of a regular space and a kernel-dependent space.

• Least-squares Galerkin form is obtained and the regularity theorem is established.

• A kernel-capture FE scheme is designed and its optimal convergence is proved.

摘要

•Prove that two-side fractional operator is surjective from solution space to L2.•Solution space is a sum of a regular space and a kernel-dependent space.•Least-squares Galerkin form is obtained and the regularity theorem is established.•A kernel-capture FE scheme is designed and its optimal convergence is proved.

论文关键词：Fractional diffusion equation,Variable-Coefficient,Space decomposition,Solvability and regularity,Least-Squares mixed finite element,Convergence

论文评审过程：Received 1 April 2020, Revised 16 January 2021, Accepted 19 March 2021, Available online 29 April 2021, Version of Record 29 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126229