Convergence Analysis of a Discontinuous Finite Element Formulation Based on Second Order Derivatives

Abstract

A new Discontinuous Galerkin Formulation is introduced for the elliptic reaction-diffusion problem that incorporates local second order distributional derivatives. The corresponding bilinear form satisfies both coercivity and continuity properties on the broken Hilbert space of H(sup 2) functions. For piecewise polynomial approximations of degree p >/= 2, optimal uniform h and p convergence rates are obtained in the broken H(sup 1) and H(sup 2) norms. Convergence in L(sup 2) is optimal for p >/= 3, if the computational mesh is strictly rectangular. If the mesh consists of skewed elements, then optimal convergence is only obtained if the corner angles satisfy a given regularity condition. For p = 2, only suboptimal h convergence rates in L(sup 2) are obtained and for linear polynomial approximations the method does not converge.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2004
Accession Number
ADA439718

Entities

People

  • Albert Romkes
  • J. T. Oden
  • Serge Prudhomme

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Coercivity
  • Continuity
  • Convergence
  • Equations
  • Galerkin Method
  • Geometry
  • Hilbert Space
  • Identities
  • Inequalities
  • Information Operations
  • Interpolation
  • Polygons
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space