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An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods

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Abstract

This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements using the weak Galerkin finite element methods. By leveraging the Schur complement of the weak Galerkin method, this extension not only preserves the same degrees of freedom as the Morley element on triangular elements but also expands its applicability to general polytopal elements. The numerical scheme is devised by locally constructing weak tangential derivatives and weak second-order partial derivatives. Error estimates for the numerical approximation are established in both the energy norm and the \(L^2\) norm. A series of numerical experiments are conducted to validate the theoretical developments.

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Authors and Affiliations

  1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Dan Li

  2. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Chunmei Wang

  3. Division of Mathematical Sciences, National Science Foundation, Alexandria, VA, 22314, USA

    Junping Wang

Authors
  1. Dan Li
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  2. Chunmei Wang
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  3. Junping Wang
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Correspondence to Chunmei Wang.

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The research of Dan Li was supported by Jiangsu Funding Program for Excellent Postdoctoral Talent (Grant No. 2023ZB271), China Postdoctoral Science Foundation (Grant No. 2023M741763), Postdoctoral Fellowship Program of CPSF (Grant No. GZB20230311), National Natural Science Foundation of China (Grants No. 12071227 and No. 12371369), and National Key Research and Development Program of China (Grant No. 2020YFA0713803).

The research of Chunmei Wang was partially supported by National Science Foundation Grant DMS-2136380.

The research of Junping Wang was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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Li, D., Wang, C. & Wang, J. An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods. J Sci Comput 100, 27 (2024). https://doi.org/10.1007/s10915-024-02580-8

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  • DOI: https://doi.org/10.1007/s10915-024-02580-8

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