Yadav, Sangita (2013) SUPERCONVERGENT DISCONTINUOUS GALERKINMETHODS FOR NONLINEAR ELLIPTIC EQUATIONS. MATHEMATICS OF COMPUTATION, 82 (283). pp. 1297-1335.
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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.
|Subjects:||Q Science > QA Mathematics|
|Deposited By:||Mr. Ramniwas Saini|
|Deposited On:||15 Sep 2019 09:25|
|Last Modified:||15 Sep 2019 09:25|
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