Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

Abstract

In this paper, we present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of $\mathcal{O}(h)$ order in energy norm and of $\mathcal{O}(h^2)$ order in $L^2$ norm on general $d$-rectangular grids. Moreover, when the grid is uniform, the convergence rate can be of $\mathcal{O}(h^2)$ order in energy norm, and the convergence rate in $L^2$ norm is still of $\mathcal{O}(h^2)$ order, which can not be improved. Numerical examples are presented to demonstrate our theoretical results.

This paper has been withdrawn by the author due to some rewrittings of the proof

References in corpus (2)

• Nonconforming finite element methods on quadrilateral meshes
• Superconvergence of both two and three dimensional rectangular Morley elements for biharmonic equations

Cited by in corpus (2)

• Lowest-degree robust finite element scheme for a fourth-order elliptic singular perturbation problem on rectangular grids
• Optimal quadratic element on rectangular grids for $H^1$ problems