Record Details

SUPERCONVERGENT DISCONTINUOUS GALERKIN METHODS FOR NONLINEAR ELLIPTIC EQUATIONS

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title SUPERCONVERGENT DISCONTINUOUS GALERKIN METHODS FOR NONLINEAR ELLIPTIC EQUATIONS
 
Creator YADAV, S
PANI, AK
PARK, EJ
 
Subject FINITE-ELEMENT METHODS
APPROXIMATION-THEORY
NONMONOTONE TYPE
PDES
 
Description 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 L-2-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 L-2-norm. These results confirm superconvergent results for linear elliptic problems.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2014-10-14T12:32:13Z
2014-10-14T12:32:13Z
2013
 
Type Article
 
Identifier MATHEMATICS OF COMPUTATION, 82(283)1297-1335
0025-5718
1088-6842
http://dspace.library.iitb.ac.in/jspui/handle/100/14427
 
Language en