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

Gudi, Thirupathi ; Nataraj, Neela ; Pani, Amiya K. (2008) An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type Mathematics of Computation, 77 (262). pp. 731-756. ISSN 0025-5718

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Official URL: http://www.ams.org/journals/mcom/2008-77-262/S0025...

Abstract

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 H1 norm and L2 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.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:81949
Deposited On:09 Feb 2012 04:47
Last Modified:18 May 2016 23:19

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