Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations. (September 2016)

• Record Type: Journal Article
• Authors: Zhao, Y.; Zhang, Y.; Shi, D.; Liu, F.; Turner, I.
• Is Part Of: Applied mathematics letters. Volume 59(2016:Sep.)
• Page Start: 38
• Page End: 47
• Publication Date: 2016-09
• Subjects: Time-fractional diffusion equations -- Quasi-Wilson element -- L1 approximation -- Fully-discrete scheme -- Superclose and superconvergence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.03.005
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: By means of spatial quasi-Wilson nonconforming finite element and classical L 1 approximation, an unconditionally stable fully-discrete scheme for two-dimensional time fractional diffusion equations is established. Moreover, convergence results in L 2 -norm and broken H 1 -norm and the corresponding superclose and superconvergence results in spatial direction in broken H 1 -norm are obtained by use of special properties of quasi-Wilson element. At the same time, the optimal order error estimate in temporal direction is derived by dealing with fractional derivative skillfully. Finally, numerical results demonstrate that the approximate scheme provides valid and efficient way for solving the time-fractional diffusion equation.