%0 Journal Article %1 Ming2006Morley %A Ming, Wang %A Xu, Jinchao %D 2006 %J Numerische Mathematik %K 31b30-higher-dimensional-biharmonic-polyharmonic-equations 65n30-pdes-bvps-finite-elements 74k20-plates %N 1 %P 155--169 %R 10.1007/s00211-005-0662-x %T The Morley Element for Fourth Order Elliptic Equations in any Dimensions %U http://dx.doi.org/10.1007/s00211-005-0662-x %V 103 %X 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.

@article{Ming2006Morley, 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.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Ming, Wang and Xu, Jinchao}, biburl = {https://www.bibsonomy.org/bibtex/2e5750e82684b54f86545848e73f20a4c/gdmcbain}, citeulike-article-id = {14641799}, citeulike-attachment-1 = {wang_06_morley.pdf; /pdf/user/gdmcbain/article/14641799/1144992/wang_06_morley.pdf; 8ca31bdab81aba8dba20ab916fc8cbbef6052397}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00211-005-0662-x}, day = 17, doi = {10.1007/s00211-005-0662-x}, file = {wang_06_morley.pdf}, interhash = {7c3b05a9a01b947ff3d5b260c5147dec}, intrahash = {e5750e82684b54f86545848e73f20a4c}, issn = {0029-599X}, journal = {Numerische Mathematik}, keywords = {31b30-higher-dimensional-biharmonic-polyharmonic-equations 65n30-pdes-bvps-finite-elements 74k20-plates}, month = jan, number = 1, pages = {155--169}, posted-at = {2018-10-02 02:36:22}, priority = {0}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {The {M}orley Element for Fourth Order Elliptic Equations in any Dimensions}, url = {http://dx.doi.org/10.1007/s00211-005-0662-x}, volume = 103, year = 2006 }