<Emphasis Type="Italic">hp</Emphasis>-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems |
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Authors: | Thirupathi Gudi Neela Nataraj Amiya K Pani |
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Institution: | (1) Industrial Mathematics Group, Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 076, India |
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Abstract: | In this paper, we have analyzed a one parameter family of hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems with Dirichlet boundary conditions. These methods depend on the values of the parameter , where θ = + 1 corresponds to the nonsymmetric and θ = −1 corresponds to the symmetric interior penalty methods when and f(u,∇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 . 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 θ = −1 is derived. Numerical experiments are presented to illustrate the theoretical results.
Supported by DST-DAAD (PPP-05) project. |
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Keywords: | 65N12 65N30 65N15 |
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