Minimal consistent finite element space for the biharmonic equation on quadrilateral grids

TL;DR

This paper introduces a minimal-degree finite element space on quadrilateral grids that ensures consistent discretization for solving biharmonic equations, optimizing computational efficiency.

Contribution

It presents a novel finite element space of piecewise quadratic polynomials that is minimal for the variational formulation of the biharmonic equation on quadrilateral grids.

Findings

Provides a finite element space that guarantees consistency for biharmonic problems.

Achieves minimal polynomial degree for the finite element space on quadrilateral grids.

Enhances computational efficiency for biharmonic equation discretization.

Abstract

In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise quadratic polynomials and is of minimal degree for the variational problem.