Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations. (15th March 2017)

• Record Type: Journal Article
• Authors: Zhao, Yanmin; Zhang, Yadong; Liu, F.; Turner, I.; Tang, Yifa; Anh, V.
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 6(2017)
• Page Start: 1087
• Page End: 1099
• Publication Date: 2017-03-15
• Subjects: Multi-term time-fractional diffusion equation -- Finite element method -- L1 approximation -- Stability -- Convergence and superconvergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.05.005
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Using finite element method in spatial direction and classical L 1 approximation in temporal direction, a fully-discrete scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O ( h 2 + τ 2 − α ) for the original variable in H 1 -norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where h and τ are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results.