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A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem

Author

Listed:
  • Yuan Bao

    (School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China)

  • Sibo Yang

    (School of Information Science and Technology, Dalian Maritime University, Dalian 116026, China)

Abstract

In this work, we construct a theoretical framework to develop non C 0 Morley type nonconforming high-convergence elements for biharmonic problems. For each element domain, P 3 should be included in the space of shape functions. Besides the degrees of freedom of Morley elements, we add the integrals and first-order moments of the normal derivatives on edges. The choice of degrees of freedom and shape function space guarantees the possibility of improving the convergence order. As an application, we specifically construct a Morley type element on triangular meshes. Lastly, numerical experiments are carried out to verify the feasibility of the element.

Suggested Citation

  • Yuan Bao & Sibo Yang, 2024. "A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem," Mathematics, MDPI, vol. 12(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3199-:d:1497398
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