Galerkin Methods for Parabolic and Schrödinger Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics

DOI10.1137/070710858zbMath1410.76145arXiv0904.3900OpenAlexW1970912568MaRDI QIDQ3584622

Georgios E. Zouraris, Dimitra Antonopoulou, Vassilios A. Dougalis

Publication date: 30 August 2010

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.3900

zbMATH Keywords

error estimates finite element methods parabolic equation noncylindrical domain parabolic approximation underwater acoustics dynamical boundary condition Crank-Nicolson time stepping linear Schrödinger evolution equation rigid bottom boundary condition

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10) 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 (8)

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation ⋮ A stochastic nonlinear differential propagation model for underwater acoustic propagation: theory and solution ⋮ A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics ⋮ Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrodinger Equation on the Rectangular Mesh ⋮ Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method ⋮ A finite difference method for the wide-angle “parabolic” equation in a waveguide with downsloping bottom ⋮ 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

This page was built for publication: Galerkin Methods for Parabolic and Schrödinger Equations with Dynamical Boundary Conditions and Applications to Underwater Acoustics