Abstract
In this paper, based on Alikhanov’s L2- $$1_\sigma $$ high-order approximation and anisotropic finite element methods, a fully discrete scheme for time fractional variable coefficient diffusion equations on anisotropic meshes is presented. Firstly, we prove that the discrete scheme is unconditionally stable in $$H^1$$ -norm, then the results of convergence in $$L_2$$ -norm and superclose in $$H^1$$ -norm are derived by combining interpolation with projection, and then, the superconvergence in $$H^1$$ -norm is obtained by using interpolation post-processing technique. In addition, it is worth mentioning the key technology of combining interpolation and projection. If interpolation or projection is used alone, the results of this article cannot be obtained. Finally, numerical examples are provided to verify the correctness of theoretical analysis.
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