Study of Superconvergence by a Computer-Based Approach. Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations

Abstract

This paper addresses the problem of existence of the superconvergence points by a computer based proof. We prove a basic mathematical theorem that the superconvergence point exists if and only if it can be found by certain numerical algorithm. We address the problem of the superconvergence points for the gradient of the finite element solution of the Laplace and Poisson equations. Our study shows that the sets of superconvergence points are very different for these two cases. We consider triangular as well as quadrilateral elements of degree p, 1 < or = p < or = 7. In the case of quadrilateral elements we analyze, among others, the tensor-product and the serendipity elements.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1993
Accession Number
ADA277537

Entities

People

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

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Engineering
  • Equations
  • Geometry
  • Maryland
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Physical Sciences
  • Polynomials
  • Theorems
  • Triangles
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

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