Analysis of key steps in numerical calculation of virtual element method for second-order elliptic problem

Ling Li; Jiaxin Wei; Chunyan Niu; Shicang Song; Jianjun Wan

doi:10.1117/12.3036979

21 July 2024 Analysis of key steps in numerical calculation of virtual element method for second-order elliptic problem

Ling Li, Jiaxin Wei, Chunyan Niu, Shicang Song, Jianjun Wan

Proceedings Volume 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024); 132190E (2024) https://doi.org/10.1117/12.3036979
Event: 4th International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2024), 2024, Kaifeng, China

Abstract

The virtual element method has special advantage in grid construction. The interpolation functions on elements have no explicit expression, so the method is called "virtual". This leads to a series of problems in concrete calculation, and we need to map the solution function, trial function and load function to the polynomial space through the projection operator. Then, the projection functions were brought into the variational formulation to execute computation. In this paper, the virtual element method of the second-order elliptic problem is taken as an example, and the key steps such as the calculation of projection matrix and projection of functions mentioned above are discussed. In particular, we give the detailed implementation of these key steps. Finally, a numerical example is given, which verifies the correctness of the analysis results in this paper.

Citation Download Citation

Ling Li, Jiaxin Wei, Chunyan Niu, Shicang Song, and Jianjun Wan "Analysis of key steps in numerical calculation of virtual element method for second-order elliptic problem", Proc. SPIE 13219, Fourth International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2024), 132190E (21 July 2024); https://doi.org/10.1117/12.3036979

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