hp-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems
DSpace at IIT Bombay
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Title |
hp-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems
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Creator |
GUDI, T
NATARAJ, N PANI, AK |
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Subject |
finite-element-method
approximation-theory diffusion-problems |
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Description |
In this paper, we have analyzed a one parameter family of hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems -del center dot a(u, del u) + f ( u,del u) = 0 with Dirichlet boundary conditions. These methods depend on the values of the parameter theta epsilon[-1, 1], where theta = + 1 corresponds to the nonsymmetric and theta = -1 corresponds to the symmetric interior penalty methods when a( u,del u) =del u and f ( u,del u) = - f, that is, for the Poisson problem. The error estimate in the broken H-1 norm, which is optimal in h ( mesh size) and suboptimal in p ( degree of approximation) is derived using piecewise polynomials of degree p >= 2, when the solution u epsilon H-5/2(Omega). In the case of linear elliptic problems also, this estimate is optimal in h and suboptimal in p. Further, optimal error estimate in the L-2 norm when theta= -1 is derived. Numerical experiments are presented to illustrate the theoretical results.
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Publisher |
SPRINGER
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Date |
2011-08-29T13:56:21Z
2011-12-26T12:58:37Z 2011-12-27T05:48:51Z 2011-08-29T13:56:21Z 2011-12-26T12:58:37Z 2011-12-27T05:48:51Z 2008 |
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Type |
Article
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Identifier |
NUMERISCHE MATHEMATIK, 109(2), 233-268
0029-599X http://dx.doi.org/10.1007/s00211-008-0137-y http://dspace.library.iitb.ac.in/xmlui/handle/10054/12102 http://hdl.handle.net/10054/12102 |
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Language |
en
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