Name
Title | ||
|---|---|---|
Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains |
Abstract | ||
|---|---|---|
The convergence of a discontinuous Galerkin method for the linear Schrödinger equation in non-cylindrical domains of $${\mathbb{R}^m}$$, m ≥ 1, is analyzed in this paper. We show the existence of the resulting approximations and prove stability and error estimates in finite element spaces of general type. When m = 1 the resulting problem is related to the standard narrow angle ‘parabolic’ approximation of the Helmholtz equation, as it appears in underwater acoustics. In this case we investigate theoretically and numerically the order of convergence using finite element spaces of piecewise polynomial functions. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s00211-010-0296-5 | Numerische Mathematik |
Keywords | Field | DocType |
general type,piecewise polynomial function,discontinuous galerkin method,dinger equation,finite element space,resulting problem,error estimate,non-cylindrical domain,helmholtz equation,linear schr,finite element,underwater acoustics,order of convergence | Discontinuous Galerkin method,Mathematical optimization,Polynomial,Mathematical analysis,Schrödinger equation,Finite element method,Helmholtz equation,Rate of convergence,Partial differential equation,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
115 | 4 | 0945-3245 |
Citations | PageRank | References |
3 | 0.53 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| D. C. Antonopoulou | 1 | 8 | 2.99 |
| M. Plexousakis | 2 | 28 | 3.48 |