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An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type

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Title An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type
 
Creator GUDI, T
NATARAJ, N
PANI, AK
 
Subject finite-element-method
approximation-theory
diffusion-problems
hp-finite elements
local discontinuous galerkin method
second order quasilinear elliptic problems
error estimates
order of convergence
 
Description In this paper, an hp-local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On hp-quasiuniform meshes, using the Brouwer 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 broken H-1 norm and L-2 norm which are optimal in h, suboptimal in p are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2011-07-16T18:26:26Z
2011-12-26T12:49:54Z
2011-12-27T05:35:42Z
2011-07-16T18:26:26Z
2011-12-26T12:49:54Z
2011-12-27T05:35:42Z
2008
 
Type Article
 
Identifier MATHEMATICS OF COMPUTATION, 77(262), 731-756
0025-5718
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4494
http://hdl.handle.net/10054/4494
 
Language en