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On the convergence and superconvergence for a class of two-dimensional time fractional reaction-subdiffusion equations |
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| Authors: | Yabing Wei Yanmin Zhao Hu Chen Fenling Wang Shujuan Lü |
| Institution: | 1. School of Mathematical Sciences, Beihang University, Beijing, China
Contribution: Writing - original draft;2. School of Science, Xuchang University, Xuchang, China;3. School of Mathematical Sciences, Ocean University of China, Qingdao, China Contribution: Methodology;4. School of Science, Xuchang University, Xuchang, China Henan Joint International Research Laboratory of High Performance Computation for Complex Systems, Xuchang, China Contribution: Writing - review & editing;5. School of Mathematical Sciences, Beihang University, Beijing, China |
| Abstract: | This paper analyzes a class of two-dimensional (2-D) time fractional reaction-subdiffusion equations with variable coefficients. The high-order L2-1σ time-stepping scheme on graded meshes is presented to deal with the weak singularity at the initial time t = 0, and the bilinear finite element method (FEM) on anisotropic meshes is used for spatial discretization. Using the modified discrete fractional Grönwall inequality, and combining the interpolation operator and the projection operator, the L2-norm error estimation and H1-norm superclose results are rigorously proved. The superconvergence result in the H1-norm is derived by applying the interpolation postprocessing technique. Finally, numerical examples are presented to verify the validation of our theoretical analysis. |
| Keywords: | anisotropic bilinear FEM initial singularity L2-1σ time-stepping scheme reaction-subdiffusion equations superconvergence |