Communications on Applied Mathematics and Computation >

2026 , Vol. 8 >Issue 3: 851 - 867

DOI: https://doi.org/10.1007/s42967-025-00476-4

ORIGINAL PAPERS

On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids

  • Hongying Man ,
  • Shangyou Zhang
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  • 1. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, China;
    2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

Received date: 2024-02-21

  Revised date: 2024-12-30

  Online published: 2026-05-29

Supported by

This work was subsidized by the National Natural Science Foundation of China (No. 12361078) and the Guangxi Natural Science Foundation of China (Nos. 2018JJB110062, 2019AC20062, 2021JJB110006, and 2021AC19147).

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Abstract

This paper is to prove one-order superconvergence of both stress and displacement of a conforming symmetric mixed finite element on uniform n-square grids, for the linear elasticity equation in the Hellinger-Reissner variational formulation. Numerical examples on 2D and 3D uniform square grids are computed, verifying the theory.

Key words： Mixed finite element; Linear elasticity; Conforming finite element; Superconvergence; Square grids

Cite this article

Hongying Man , Shangyou Zhang . On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids[J]. Communications on Applied Mathematics and Computation, 2026 , 8(3) : 851 -867 . DOI: 10.1007/s42967-025-00476-4

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