A stabilizer‐free weak Galerkin finite element method to variable‐order time fractional diffusion equation in multiple space dimensions. Issue 3 (29th November 2022)

• Record Type: Journal Article
• Authors: Ma, Jie; Gao, Fuzheng; Du, Ning
• Is Part Of: Numerical methods for partial differential equations. Volume 39:Issue 3(2023)
• Page Start: 2096
• Page End: 2114
• Publication Date: 2022-11-29
• Subjects: error estimate -- fast algorithm -- stabilizer‐free weak Galerkin finite element method -- variable‐order Caputo time‐fractional diffusion equation; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22959
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: We study a fully‐discrete stabilizer‐free weak Galerkin (SFWG) finite element method for the initial‐boundary value problem of variable‐order Caputo time‐fractional diffusion equation. Optimal convergence order in L 2 $$ {L}_2 $$ norm for L 1 $$ L1 $$ fully‐discrete SFWG scheme is obtained. Furthermore, we develop a fast evaluation algorithm to improve the computational efficiency. Numerical experiments are performed to verify theoretical results.