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The Morley element for fourth order elliptic equations in any dimensions

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Abstract

In this paper, the well-known nonconforming Morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion. The general n-dimensional Morley element consists of all quadratic polynomials defined on each n-simplex with degrees of freedom given by the integral average of the normal derivative on each (n-1)-subsimplex and the integral average of the function value on each (n-2)-subsimplex. Explicit expressions of nodal basis functions are also obtained for this element on general n-simplicial grids. Convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation.

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Authors and Affiliations

  1. LMAM, The School of Mathematical Sciences, Peking University,  

    Wang Ming & Jinchao Xu

  2. Department of Mathematics, Pennsylvania State University,  

    Jinchao Xu

Authors
  1. Wang Ming
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  2. Jinchao Xu
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Correspondence to Jinchao Xu.

Additional information

The work was supported by the National Natural Science Foundation of China (10571006).

This work was supported in part by NSF DMS-0209497 and NSF DMS-0215392 and the Changjiang Professorship through Peking University.

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Ming, W., Xu, J. The Morley element for fourth order elliptic equations in any dimensions. Numer. Math. 103, 155–169 (2006). https://doi.org/10.1007/s00211-005-0662-x

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  • DOI: https://doi.org/10.1007/s00211-005-0662-x

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