Paper Info
Title
hp-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems
Abstract
In this paper, we have analyzed a one parameter family of hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems $$-\nabla \cdot {\rm a} (u, \nabla u) + f (u, \nabla u) = 0$$ with Dirichlet boundary conditions. These methods depend on the values of the parameter $$\theta\in[-1,1]$$, where θ =  + 1 corresponds to the nonsymmetric and θ = −1 corresponds to the symmetric interior penalty methods when $${\rm a}(u,\nabla u)={\nabla}u$$ 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 $$u\in H^{5/2}(\Omega)$$. 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 θ = −1 is derived. Numerical experiments are presented to illustrate the theoretical results.
Year
DOI
Venue
2008
10.1007/s00211-008-0137-y
Numerische Mathematik
Keywords
Field
DocType
parameter family,error estimate,linear elliptic problem,broken h,dirichlet boundary condition,nonlinear elliptic boundary value,optimal error estimate,hp-discontinuous galerkin method,degree p,nabla u,poisson problem,discontinuous galerkin method,elliptic boundary value problem
Discontinuous Galerkin method,Boundary value problem,Nabla symbol,Mathematical optimization,Mathematical analysis,Galerkin method,Dirichlet boundary condition,Norm (mathematics),Partial differential equation,Mathematics,Elliptic curve
Journal
Volume
Issue
ISSN
109
2
0945-3245
Citations 
PageRank 
References 
7
0.50
7
Authors
3
Name
Order
Citations
PageRank
Thirupathi Gudi113514.43
Neela Nataraj25810.77
Amiya Kumar Pani37113.73