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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/11963

Title: Discontinuous galerkin methods for quasi-linear elliptic problems of nonmonotone type
Authors: GUDI, T
PANI, AK
Keywords: finite-element-method
approximation-theory
p-version
Issue Date: 2007
Publisher: SIAM PUBLICATIONS
Citation: SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(1), 163-192
Abstract: 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.
URI: http://dx.doi.org/10.1137/050643362
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11963
http://hdl.handle.net/10054/11963
ISSN: 0036-1429
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