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Yadav, Sangita (2013) SUPERCONVERGENT DISCONTINUOUS GALERKINMETHODS FOR NONLINEAR ELLIPTIC EQUATIONS. MATHEMATICS OF COMPUTATION, 82 (283). pp. 1297-1335.

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Official URL: https://pdfs.semanticscholar.org/bd70/4e289000ee0a...

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 supercon-vergence results for nonselfadjoint linear elliptic problems using discontinuousGalerkin methods. Further, we have extended our analysis to derive supercon-vergence results for quasilinear elliptic problems. When piecewise polynomialsof degreek≥1 are used to approximate both the potential as well as theflux, it is shown, in this article, that the error estimate for the discrete flux inL2-norm iorderk+1.Further, based on solving a discrete linear ellipticproblem at each element, a suitable postprocessing of the discrete potentialis developed and then, it is proved that the resulting post-processed potentialconverges with order of convergencek+2inL2-norm. These results confirmsuperconvergent results for linear elliptic problems.

Item Type:Article
Subjects:Q Science > QA Mathematics
Divisions:Mathematics
ID Code:2336
Deposited By:Mr. Ramniwas Saini
Deposited On:15 Sep 2019 09:25
Last Modified:15 Sep 2019 09:25

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