Superconvergence of simple conforming mixed finite elements for linear elasticity on rectangular grids in any space dimension

TL;DR

This paper proves superconvergence properties of a simple family of conforming mixed finite elements for linear elasticity problems on rectangular grids across any dimension, using novel analytical tools.

Contribution

It introduces new interpolation, expansion, and iterative methods to establish superconvergence for first-order mixed finite elements in elasticity.

Findings

Superconvergence is achieved for the proposed finite elements.

The analysis applies to any space dimension.

New analytical techniques improve understanding of finite element superconvergence.

Abstract

This paper is to prove superconvergence of a family of simple conforming mixed finite elements of first orderfor the linear elasticity problem with the Hellinger--Reissner variational formulation. The analysis is based on three main ingredients: a new interpolation operator, a new expansion method, and a new iterative argument for superconvergence analysis.