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An Error Analysis Method SPP-BEAM and a Construction Guideline of Nonconforming Finite Elements for Fourth Order Elliptic Problems

An Error Analysis Method SPP-BEAM and a Construction Guideline of Nonconforming Finite Elements for Fourth Order Elliptic Problems
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Year:    2020

Author:    Jun Hu, Shangyou Zhang

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 195–222

Abstract

Under two hypotheses of nonconforming finite elements of fourth order elliptic problems, we present a side–patchwise projection based error analysis method (SPP–BEAM for short). Such a method is able to avoid both the regularity condition of exact solutions in the classical error analysis method and the complicated bubble function technique in the recent medius error analysis method. In addition, it is universal enough to admit generalizations. Then, we propose a sufficient condition for these hypotheses by imposing a set of in some sense necessary degrees of freedom of the shape function spaces. As an application, we use the theory to design a $P_3$ second order triangular $H^2$ non-conforming element by enriching two $P_4$ bubble functions and, another $P_4$ second order triangular $H^2$ nonconforming finite element, and a $P_3$ second order tetrahedral $H^2$ non-conforming element by enriching eight $P_4$ bubble functions, adding some more degrees of freedom.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1811-m2018-0162

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 195–222

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Nonconforming finite element A priori error analysis Biharmonic equation.

Author Details

Jun Hu

Shangyou Zhang

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