Superconvergent discontinuous galerkin methods for nonlinear elliptic equations

Sangita Yadav, Amiya K. Pani, Eun Jae Park

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9 Citations (Scopus)

Abstract

Based on the analysis of Cockburn et al. [Math. Comp. 78 (2009), pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence results for nonselfadjoint linear elliptic problems using discontinuous Galerkin methods. Further, we have extended our analysis to derive superconvergence results for quasilinear elliptic problems. When piecewise polynomials of degree k ≤ 1 are used to approximate both the potential as well as the flux, it is shown, in this article, that the error estimate for the discrete flux in L2-norm is of order k + 1. Further, based on solving a discrete linear elliptic problem at each element, a suitable postprocessing of the discrete potential is developed and then, it is proved that the resulting post-processed potential converges with order of convergence k + 2 in L2-norm. These results confirm superconvergent results for linear elliptic problems.

Original languageEnglish
Pages (from-to)1297-1335
Number of pages39
JournalMathematics of Computation
Volume82
Issue number283
DOIs
Publication statusPublished - 2013 May 30

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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