An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type
DSpace at IIT Bombay
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Title |
An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type
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Creator |
GUDI, T
NATARAJ, N PANI, AK |
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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 |
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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.
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Publisher |
AMER MATHEMATICAL SOC
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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 |
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Type |
Article
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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 |
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Language |
en
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