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A weak Galerkin method with rectangle partitions for the Signorini problem

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Abstract

A weak Galerkin method with rectangle partitions is built for solving the Signorini problem in two-dimensional space. In the method, we use a new combination of totally discontinuous piecewise bilinear polynomials defined on rectangle elements and piecewise linear polynomials defined on edge elements. Then, we obtain the optimal error estimates in both the newly defined h-norm and the standard \(L^{2}\)-norm for the weak Galerkin method. Moreover, we study some properties about the mass matrix in detail. Finally, some numerical examples are given to demonstrate the theoretical conclusions.

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Acknowledgements

The authors are greatly indebted to the referees for useful comments. This work is supported by the National Natural Science Foundation of China (11771112, 12071100).

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Jingjun Zhao, Zhiqiang Lv & Yang Xu

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  1. Jingjun Zhao
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  2. Zhiqiang Lv
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  3. Yang Xu
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Correspondence to Yang Xu.

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Communicated by Abimael Loula.

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Zhao, J., Lv, Z. & Xu, Y. A weak Galerkin method with rectangle partitions for the Signorini problem. Comp. Appl. Math. 41, 207 (2022). https://doi.org/10.1007/s40314-022-01883-6

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  • DOI: https://doi.org/10.1007/s40314-022-01883-6

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