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Discontinuous galerkin methods for quasi-linear elliptic problems of nonmonotone type

DSpace at IIT Bombay

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Title Discontinuous galerkin methods for quasi-linear elliptic problems of nonmonotone type
 
Creator GUDI, T
PANI, AK
 
Subject finite-element-method
approximation-theory
p-version
hp-finite elements
discontinuous galerkin methods
second order quasi-linear elliptic problems
optimal estimates
brouwer's fixed point theorem
 
Description In this paper, both symmetric and nonsymmetric interior penalty discontinuous hp-Galerkin methods are applied to a class of quasi-linear elliptic problems which are of nonmonotone type. Using Brouwer's fixed point theorem, it is shown that the discrete problem has a solution, and then, using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in the broken H-1-norm, which are optimal in h and suboptimal in p, are derived. Moreover, on a regular mesh an hp-error estimate for the L-2-norm is also established. Finally, numerical experiments illustrating the theoretical results are provided.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:49:49Z
2011-12-26T12:58:24Z
2011-12-27T05:48:17Z
2011-08-29T04:49:49Z
2011-12-26T12:58:24Z
2011-12-27T05:48:17Z
2007
 
Type Article
 
Identifier SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(1), 163-192
0036-1429
http://dx.doi.org/10.1137/050643362
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11963
http://hdl.handle.net/10054/11963
 
Language en