Study of Superconvergence by a Computer-Based Approach: Superconvergence of the Gradient of the Displacement, The Strain and Stress in Finite Element Solutions for Plane Elasticity.

Abstract

In 1 we addressed the problem of existence of superconvergence points by a computer-based proof and we gave a detailed study of the superconvergence points for the components of the gradient in finite element solutions for Laplace's and Poisson's equations. Here we employ the same approach to study the superconvergence for the gradient of the displacement, the strain and the stress for finite element solutions of the equations of plane elasticity. We give the superconvergence points for the components of the gradient of the displacement, the strain and stress for meshes of triangles and squares of degree p, 1 < or = p < or = 4. For the meshes of triangles we investigated the effect of the topology of the mesh by considering four mesh-patterns which typically occur in practical meshes, while in the case of square elements we studied the effect of the element-type (tensor-product, serendipity or other).

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1994
Accession Number
ADA279885

Entities

People

  • C. S. Upadhyay
  • Ivo Babuška
  • S. K. Gangaraj
  • T. Strouboulis

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Elastic Properties
  • Engineering
  • Equations
  • Families (Human)
  • Government (Foreign)
  • Mathematics
  • Military Research
  • Nonlinear Differential Equations
  • Numerical Analysis
  • Physical Sciences
  • Standards
  • Theorems
  • Topology

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)