A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems

Bernardo Cockburn, Bo Dong, Johnny Guzmán

Research output: Contribution to journalArticlepeer-review

164 Scopus citations

Abstract

We identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree k ≧ 0 for both the potential as well as the flux, the order of convergence in L2 of both unknowns is k + 1. Moreover, both the approximate potential as well as its numerical trace superconverge in L2-like norms, to suitably chosen projections of the potential, with order k + 2. This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order K + 2 in L2. The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.

Original languageEnglish (US)
Pages (from-to)1887-1916
Number of pages30
JournalMathematics of Computation
Volume77
Issue number264
DOIs
StatePublished - Oct 2008

Keywords

  • Discontinuous Galerkin methods
  • Hybridization
  • Second-order elliptic problems
  • Superconvergence

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