Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient

Abstract

The goal of this paper is to discuss high accuracy analysis of a fully-discrete scheme for 2D multi-term time fractional wave equations with variable coefficient on anisotropic meshes by approximating in space by linear triangular finite element method and in time by Crank-Nicolson scheme. The stability is firstly proved unconditionally. In the analysis of superclose properties, how to deal with the item for variable coefficient is the main difficulty. In order to do this, a new projection operator is defined and the relationship between the proposed projection operator and interpolation operator about linear triangular finite element is deduced. Consequently, the global superconvergence result is obtained by use of interpolation postprocessing technique. The numerical examples show that the proposed numerical method is highly accurate and computationally efficient.

Keywords:

• Multi-term time fractional diffusion-wave equations
• linear triangular finite element
• Crank-Nicolson approximation
• stability
• superclose and superconvergence

2010 AMS Subject Classifications:

• 65N30
• 35R11

Acknowledgments

Authors are grateful to Prof. Fawang Liu and the reviews for their valuable advice.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

We appreciate support of the National Natural Science Foundation of China (Nos. 11771438, 11471296), the Key Scientific Research Projects in Universities of Henan Province (Nos. 17A110011, 19B110013) and the Program for Scientific and Technological Innovation Talents in Universities of Henan Province (No. 19HASTIT025).