Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain

DOI10.1090/S0025-5718-2014-02900-1zbMath1309.65105OpenAlexW2095332876MaRDI QIDQ5246833

Michael Plexousakis, Georgia Karali, Georgios E. Zouraris, Dimitra Antonopoulou

Publication date: 22 April 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02900-1

zbMATH Keywords

finite element methodnoncylindrical domaina priori error estimatesunderwater acousticselliptic regularitySchrödinger-type equationRobin-type boundary conditionCrank-Nicolson time stepping

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation ⋮ Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation ⋮ Two-grid method for the two-dimensional time-dependent Schrödinger equation by the finite element method ⋮ Superconvergence analysis of bi-\(k\)-degree rectangular elements for two-dimensional time-dependent Schrödinger equation ⋮ Two-grid finite volume element method for the time-dependent Schrödinger equation ⋮ Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions ⋮ Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity ⋮ Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains
• Partial differential equations. 4th ed
• Finite Difference Schemes for the "Parabolic" Equation in a Variable Depth Environment with a Rigid Bottom Boundary Condition
• A finite difference method for the wide-angle “parabolic” equation in a waveguide with downsloping bottom
• The initial boundary value problem for the Schröudinger equation
• Heat Equation with Dynamical Boundary Conditions of Reactive Type
• Galerkin Methods for Parabolic and Schrödinger Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics
• Parabolic Wave Equation Approximations in Heterogenous Media
• Error Estimates for Finite Difference Methods for a Wide-Angle “Parabolic” Equation
• On an initial‐boundary value problem for a wide‐angle parabolic equation in a waveguide with a variable bottom
• The Mathematical Theory of Finite Element Methods
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations