, Volume 103, Issue 1, pp 155169
First online:
The Morley element for fourth order elliptic equations in any dimensions
 Wang MingAffiliated withLMAM, The School of Mathematical Sciences, Peking University
 , Jinchao XuAffiliated withLMAM, The School of Mathematical Sciences, Peking UniversityDepartment of Mathematics, Pennsylvania State University Email author
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In this paper, the wellknown nonconforming Morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion. The general ndimensional Morley element consists of all quadratic polynomials defined on each nsimplex with degrees of freedom given by the integral average of the normal derivative on each (n1)subsimplex and the integral average of the function value on each (n2)subsimplex. Explicit expressions of nodal basis functions are also obtained for this element on general nsimplicial grids. Convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation.
Keywords
Nonconforming finite element Forth order elliptic equation Biharmonic Morley element Title
 The Morley element for fourth order elliptic equations in any dimensions
 Journal

Numerische Mathematik
Volume 103, Issue 1 , pp 155169
 Cover Date
 200603
 DOI
 10.1007/s002110050662x
 Print ISSN
 0029599X
 Online ISSN
 09453245
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Nonconforming finite element
 Forth order elliptic equation
 Biharmonic
 Morley element
 Industry Sectors
 Authors

 Wang Ming ^{(1)}
 Jinchao Xu ^{(1)} ^{(2)}
 Author Affiliations

 1. LMAM, The School of Mathematical Sciences, Peking University,
 2. Department of Mathematics, Pennsylvania State University,