Dr. Yabing Wei (Jiangsu University)

唐贻发 研究员

Superconvergence analysis of nonconforming finite element method for two-dimensional time-fractional Allen-Cahn equation

8月10日（周一）14:30-15:30，南楼602

In this report, we investigate the numerical solution of the time-fractional Allen-Cahn equation with variable diffusion coefficients. A fully discrete approximation is presented by the L2-1_σscheme on graded meshes and spatial high precision nonconforming finite element method (FEM). The nonlinear term is treated with the Newton linearization method. Based on the modified discrete fractional Grönwall inequality, we rigorously prove that the proposed scheme can achieve optimal convergence accuracy in both time and space directions. Furthermore, the H^1-norm global superconvergence result is obtained through the interpolation postprocessing technique. Finally, numerical experiments confirm the correctness of our theoretical analysis.

报告人简介：魏亚冰于2023年在北京航空航天大学获得博士学位；于2021.12-2022.12期间访问新加坡南洋理工大学；2023.06-至今在江苏大学数学科学学院工作。魏亚冰博士主要从事分数阶偏微分方程的数值算法研究，近年来在国内外期刊发表论文十余篇，主持省自然科学基金项目一项。