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Weak Galerkin finite element methods with or without stabilizers

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Abstract

The purpose of this paper is to investigate the connections between the weak Galerkin (WG) methods with and without stabilizers. The choices of stabilizers directly affect the convergence rates of the corresponding WG methods in general. However, we observed that the convergence rates are independent of the choices of stabilizers for these WG elements with stabilizers being optional. In this paper, we will verify such phenomena theoretically as well as numerically.

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Funding

This research was supported in part by National Science Foundation Grant DMS-1620016.

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Authors and Affiliations

  1. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiaoshen Wang & Xiu Ye

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Shangyou Zhang

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  1. Xiaoshen Wang
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  2. Xiu Ye
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  3. Shangyou Zhang
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Correspondence to Shangyou Zhang.

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Wang, X., Ye, X. & Zhang, S. Weak Galerkin finite element methods with or without stabilizers. Numer Algor 88, 1361–1381 (2021). https://doi.org/10.1007/s11075-021-01079-9

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  • DOI: https://doi.org/10.1007/s11075-021-01079-9

Keywords

Mathematics Subject Classication (2010)