Volume 12, Issue 1
The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations

Adv. Appl. Math. Mech., 12 (2020), pp. 164-188.

Published online: 2019-12

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• 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.

• Keywords

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

65M60, 65M15, 65M12

xiuli16@email.jlu.edu.cn (Xiuli Wang)

zhaiql@pku.edu.cn (Qilong Zhai)

zhangran@jlu.edu.cn (Ran Zhang)

szhang@udel.edu (Shangyou Zhang)

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• TXT
@Article{AAMM-12-164, author = {Wang , Xiuli and Zhai , Qilong and Zhang , Ran and Zhang , Shangyou }, title = {The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {12}, number = {1}, pages = {164--188}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0088}, url = {http://global-sci.org/intro/article_detail/aamm/13423.html} }
TY - JOUR T1 - The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations AU - Wang , Xiuli AU - Zhai , Qilong AU - Zhang , Ran AU - Zhang , Shangyou JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 164 EP - 188 PY - 2019 DA - 2019/12 SN - 12 DO - http://dor.org/10.4208/aamm.OA-2019-0088 UR - https://global-sci.org/intro/article_detail/aamm/13423.html KW - Integro-differential problem, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence. AB -

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.

Xiuli Wang, Qilong Zhai, Ran Zhang & Shangyou Zhang. (2019). The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations. Advances in Applied Mathematics and Mechanics. 12 (1). 164-188. doi:10.4208/aamm.OA-2019-0088
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