On optimal finite element schemes for biharmonic equation

Abstract

In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation with optimal convergence rates on general shape-regular triangulations. Therefore, it is proved that optimal finite element schemes of arbitrary order for planar biharmonic equation can be constructed on general shape-regular triangulations.

References in corpus (2)

• Nonconforming Finite Element Spaces for $2m$-th Order Partial Differential Equations on ${\mathbb{R}}^n$ Simplicial Grids When $m=n+1$
• Minimal consistent finite element space for the biharmonic equation on quadrilateral grids

Cited by in corpus (3)

• A nodal type polynomial finite element exact sequence over quadrilaterals
• A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem
• High accuracy analysis of a nonconforming discrete Stokes complex over rectangular meshes