The p- and h-p Versions of the Finite Element Method: An Overview

Abstract

In this paper presents a survey of the state of the art of the p and h-p versions. The emphasis is on the theoretical aspects related to their use in approximating elliptic equations stemming from structural mechanics. The origins of the finite element method (FEM), like those of the spectral method, may be traced back a long time. If we understand the FEM as the application of variational principles and approximation by piecewise smooth functions, then this idea was already used by Leibnitz in 1696 (in one dimension with piecewise linear functions). In two dimensions, Schellbach used triangulation and piecewise linear functions. Nevertheless, the modern FEM era starts with a paper which demonstrated the potential for the use of the computer. Since then, more than 30,000 papers have appeared. These papers are generally based on the h- version of the FEM, where the accuracy of the approximate solution is achieved by refining the mesh while using low order polynomials on the mesh. (kr)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA216902

Entities

People

  • Ivo Babuška
  • Manil Suri

Tags

DTIC Thesaurus Topics

  • Boundary Element Methods
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computer Science
  • Differential Equations
  • Elastic Properties
  • Engineering
  • Equations
  • Finite Element Analysis
  • Fluid Mechanics
  • Materials
  • Mechanics
  • Modulus Of Elasticity
  • Numerical Analysis
  • Structural Mechanics
  • Two Dimensional

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