Convergence analysis of a discontinuous finite element formulation based on second order derivatives

Albert Romkes*, Serge Prudhomme, J. Tinsley Oden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 H2 functions. For piecewise polynomial approximations of degree p {greater than or slanted equal to} 2, optimal uniform h and p convergence rates are obtained in the broken H1 and H2 norms. Convergence in L2 is optimal for p {greater than or slanted equal to} 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 L2 are obtained and for linear polynomial approximations the method does not converge.

Original languageEnglish (US)
Pages (from-to)3461-3482
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume195
Issue number25-28
DOIs
StatePublished - May 1 2006

Keywords

  • A priori error estimates
  • Discontinuous Galerkin methods

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

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