Numerical Treatment of Differential and Integral Equations by the P and H-P Versions of the Finite Element Method

Abstract

The problem of locking , which arises in the approximation of parameters dependent problems has been extensively investigated. A general theoretical framework to analyze this phenomenon has been developed, and the locking and robustness of different finite element schemes for various problems has been characterized. Work on the p and h-p versions of the finite element method has continued. Progress here includes optimal approximation results for the p version of the boundary element method in three dimensions, an analysis of a p version mixed method for quasilinear problems, and investigation of quadrature schemes and related errors. Additional work has been conducted on singularities of solutions for the three dimensional elasticity and hydro dynamics equations in domains with edges and vertices, on the numerical evaluation of singular surface integrals in the boundary element method, and the calculation of optimal shear correction factors for plate models.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADA247202

Entities

People

  • Christoph Schwab
  • Manil Suri

Organizations

  • University of Maryland, Baltimore County

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Element Methods
  • Boundary Value Problems
  • Differential Equations
  • Elastic Properties
  • Equations
  • Finite Element Analysis
  • Geometry
  • Integral Equations
  • Integrals
  • Mathematics
  • Mechanical Properties
  • Numerical Analysis
  • Numerical Integration
  • Numerical Quadrature
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

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