The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations

Authors

  • Xiuli Wang College of Computer Science and Technology, Jilin University, Changchun 130012, Jilin, China
  • Qilong Zhai School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Ran Zhang Department of Mathematics, Jilin University, Changchun 130012, China.
  • Shangyou Zhang Department of Mathematics Science, University of Delaware, Newark 19716, USA

DOI:

https://doi.org/10.4208/aamm.OA-2019-0088

Keywords:

Integro-differential problem, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence.

Abstract

In this paper, we solve linear parabolic integral differential equations using the weak Galerkin finite element method (WG) by adding a stabilizer. The semi-discrete and fully-discrete weak Galerkin finite element schemes are constructed. Optimal convergent orders of the solution of the WG in $L^2$ and $H^1$ norm are derived. Several computational results confirm the correctness and efficiency of the method.

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Published

2020-03-06

Issue

Vol. 12 No. 1 (2020)

Section

Articles