### Electronic Research Archive

2020, Issue 2: 911-933. doi: 10.3934/era.2020048
Special Issues

# A $C^0P_2$ time-stepping virtual element method for linear wave equations on polygonal meshes

• Received: 01 February 2020 Revised: 01 April 2020
• Primary: 65M60, 65M15; Secondary: 35L20

• This paper is concerned with a $C^0P_2$ time-stepping virtual element method (VEM) for solving linear wave equations on polygonal meshes. The spatial discretization is carried out by the VEM while the temporal discretization is obtained based on the $C^0P_2$ time-stepping approach, leading to a fully discrete method. The error estimates in the $H^1$ semi-norm and $L^2$ norm are derived after detailed derivation. Finally, the numerical performance and efficiency of the proposed method is illustrated by several numerical experiments.

Citation: Jianguo Huang, Sen Lin. A $C^0P_2$ time-stepping virtual element method for linear wave equations on polygonal meshes[J]. Electronic Research Archive, 2020, 28(2): 911-933. doi: 10.3934/era.2020048

### Related Papers:

• This paper is concerned with a $C^0P_2$ time-stepping virtual element method (VEM) for solving linear wave equations on polygonal meshes. The spatial discretization is carried out by the VEM while the temporal discretization is obtained based on the $C^0P_2$ time-stepping approach, leading to a fully discrete method. The error estimates in the $H^1$ semi-norm and $L^2$ norm are derived after detailed derivation. Finally, the numerical performance and efficiency of the proposed method is illustrated by several numerical experiments.

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