A Discontinuous hp Finite Element Method for Diffusion Problems

Abstract

We present an extension of the discontinuous Galerkin method (DGM) which is applicable to the numerical solution of diffusion problems. The method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries. Within each element, arbitrary spectral approximations can be constructed with different orders p in each element. We demonstrate that the method is elementwise conservative, a property uncharacteristic of high order finite elements. For clarity, we focus on a model class of linear second-order boundary value problems, and we develop a priori error estimates, convergence proofs, and stability estimates. The results of numerical experiments on h- and p-convergence rates for representative two-dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1999
Accession Number
AD1158494

Entities

People

  • Carlos E. Baumann
  • Ivo Babuška
  • J. T. Oden

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mechanics
  • Aspect Ratio
  • Boundaries
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Continuity
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Galerkin Method
  • Hilbert Space
  • Mathematical Analysis
  • Numerical Analysis
  • Partial Differential Equations
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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