Name
Title | ||
|---|---|---|
Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain |
Abstract | ||
|---|---|---|
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography, we consider an initiala- and boundary-value problem for a general Schrodinger-type equation posed on a two space-dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank-Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L-2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method. |
Year | Venue | Keywords |
|---|---|---|
2015 | MATHEMATICS OF COMPUTATION | Schrodinger-type equation,noncylindrical domain,Robin-type boundary condition,elliptic regularity,Crank-Nicolson time stepping,finite element method,apriori error estimates,underwater acoustics |
Field | DocType | Volume |
Mathematical optimization,Mathematical analysis,Schrödinger's cat,Underwater acoustics,Finite element method,Crank–Nicolson method,Mathematics,Computation | Journal | 84 |
Issue | ISSN | Citations |
294 | 0025-5718 | 0 |
PageRank | References | Authors |
0.34 | 3 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| D. C. Antonopoulou | 1 | 8 | 2.99 |
| Georgia D. Karali | 2 | 2 | 2.25 |
| M. Plexousakis | 3 | 28 | 3.48 |
| Georgios E. Zouraris | 4 | 212 | 28.97 |