High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems.

Abstract

We develop a framework for applying high-order finite element methods to singularly-perturbed elliptic and parabolic differential systems that utilizes special quadrature rules to confine spurious effects, such as excess diffusion and non-physical oscillations, to boundary and interior layers. This approach is more suited for use with adaptive mesh-refinement and order-variation techniques than other problem-dependent methods. Quadrature rules, developed for two-point convection-diffusion and reaction-diffusion problems, are used with finite element software to solve examples involving ordinary and partial differential equations. Numerical artifacts are confined to layers for all combinations of meshes, orders, and singular perturbation parameters that were tested. Radau or Lobatto quadrature used with the finite element method to solve, respectively, convection-and reaction-diffusion problems provide the benefits of the specialized quadrature formulas and are simpler to implement.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1993
Accession Number
ADA290410

Entities

People

  • J. E. Flaherty
  • Mohammed Aiffa
  • Slimane Adjerid

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computations
  • Convection
  • Difference Equations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Mathematics
  • New York
  • Partial Differential Equations
  • Perturbations
  • Polynomials
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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