Accession Number:

ADA439718

Title:

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

Descriptive Note:

Research paper

Corporate Author:

TEXAS UNIV AT AUSTIN

Report Date:

2004-11-01

Pagination or Media Count:

32.0

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 Hsup 2 functions. For piecewise polynomial approximations of degree p 2, optimal uniform h and p convergence rates are obtained in the broken Hsup 1 and Hsup 2 norms. Convergence in Lsup 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 Lsup 2 are obtained and for linear polynomial approximations the method does not converge.

Subject Categories:

  • Numerical Mathematics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE