Academic Journal
Convergence analysis of a Schrödinger problem with moving boundary
| Τίτλος: | Convergence analysis of a Schrödinger problem with moving boundary |
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| Συγγραφείς: | Daniel G. Alfaro Vigo, Daniele C.R. Gomes, Bruno A. do Carmo, Mauro A. Rincon |
| Πηγή: | Mathematics and Computers in Simulation. 238:45-64 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Elsevier BV, 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Analysis of PDEs (math.AP) |
| Περιγραφή: | In this article, we present the mathematical analysis of the convergence of the linearized Crank-Nicolson Galerkin method for a nonlinear Schrodinger problem related to a domain with a moving boundary. The convergence analysis of the numerical method is carried out for both semi-discrete and fully discrete problems. An optimal error estimate in the $L^2$-norm with order ${O}(τ^2+ h^s),~ 2\leq s\leq r$, where $h$ is the finite element mesh size parameter, $τ$ is the time step, and $r-1$ represents the degree of the finite element polynomial basis. Numerical simulations are provided to confirm the consistency between theoretical and numerical results, validating the method and the order of convergence for different degrees $p\geq 1$ of the Lagrange polynomials and also for Hermite polynomials (degree $p=3$), which form the basis of the approximate solution. |
| Τύπος εγγράφου: | Article |
| Γλώσσα: | English |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2025.04.042 |
| DOI: | 10.48550/arxiv.2410.08910 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2410.08910 |
| Rights: | Elsevier TDM CC BY NC ND |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....ed16ebd559e1d2d5c8f92bccf0c7d1fa |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 03784754 |
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| DOI: | 10.1016/j.matcom.2025.04.042 |