Name
Title | ||
|---|---|---|
Discontinuous Galerkin Methods for Quasi-Linear Elliptic Problems of Nonmonotone Type |
Abstract | ||
|---|---|---|
In this paper, both symmetric and nonsymmetric interior penalty discontinuous $hp$-Galerkin methods are applied to a class of quasi-linear elliptic problems which are of nonmonotone type. Using Brouwer’s 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 the broken $H^1$-norm, which are optimal in $h$ and suboptimal in $p$, are derived. Moreover, on a regular mesh an $hp$-error estimate for the $L^2$-norm is also established. Finally, numerical experiments illustrating the theoretical results are provided. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/050643362 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
galerkin method,nonsymmetric interior penalty discontinuous,nonmonotone type,numerical experiment,quasi-linear elliptic problems,error estimate,discontinuous galerkin methods,discrete problem,point theorem,lipschitz continuity,discrete solution map,quasi-linear elliptic problem,discontinuous galerkin method | Discontinuous Galerkin method,Uniqueness,Mathematical optimization,Mathematical analysis,Galerkin method,Finite element method,Lipschitz continuity,Mathematics,Fixed-point theorem,Elliptic curve,Penalty method | Journal |
Volume | Issue | ISSN |
45 | 1 | 0036-1429 |
Citations | PageRank | References |
15 | 0.91 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Thirupathi Gudi | 1 | 135 | 14.43 |
| Amiya Kumar Pani | 2 | 71 | 13.73 |