Convergence of an Adaptive Mixed Finite Element Method for Kirchhoff Plate Bending Problems
SIAM Journal on Numerical Analysis
A Mixed Method for the Biharmonic Problem Based On a System of First-Order Equations
SIAM Journal on Numerical Analysis
C0-Nonconforming Triangular Prism Elements for the Three-Dimensional Fourth Order Elliptic Problem
Journal of Scientific Computing
New error estimates of the Morley element for the plate bending problems
Journal of Computational and Applied Mathematics
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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.