Paper Info
Title
An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type.
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 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.
Year
Venue
Keywords
2008
MATHEMATICS OF COMPUTATION
hp-finite elements,local discontinuous Galerkin method,second order quasilinear elliptic problems,error estimates,order of convergence
DocType
Volume
Issue
Journal
77
262
ISSN
Citations 
PageRank 
0025-5718
8
0.54
References 
Authors
5
3
Name
Order
Citations
PageRank
Thirupathi Gudi113514.43
Neela Nataraj25810.77
Amiya Kumar Pani3304.02