Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains

DOI10.1007/s00211-010-0296-5zbMath1193.65170OpenAlexW2051602955MaRDI QIDQ981650

Michael Plexousakis, Dimitra Antonopoulou

Publication date: 2 July 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-010-0296-5

zbMATH Keywords

stabilityconvergenceerror estimatesfinite elementdiscontinuous Galerkin methodHelmholtz equationunderwater acousticslinear Schrödinger equationnon-cylindrical domains

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (7)

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation ⋮ Two-grid algorithm for two-dimensional linear Schrödinger equation by the mixed finite element method ⋮ Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method ⋮ Superconvergence analysis of bi-\(k\)-degree rectangular elements for two-dimensional time-dependent Schrödinger equation ⋮ Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain ⋮ Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions ⋮ A Theoretical Analysis for a New Finite Volume Scheme for a Linear Schrödinger Evolution Equation on General Nonconforming Spatial Meshes

Uses Software

• OASES

Cites Work

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