A time- and spaceadaptive algorithm for the linear time-dependent Schrödinger equation

DOI10.1007/s002110050199zbMath0860.65097OpenAlexW2088552913MaRDI QIDQ1923297

Willy Dörfler

Publication date: 14 April 1997

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

Full work available at URL: https://doi.org/10.1007/s002110050199

zbMATH Keywords

error estimatesfinite element methodnumerical exampleslinear evolution Schrödinger equationmesh adaptive algorithm

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) 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) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Local adaptive methods for convection dominated problems ⋮ An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump ⋮ Unnamed Item ⋮ Sharp 𝐿¹ a posteriori error analysis for nonlinear convection-diffusion problems ⋮ A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method ⋮ A Posteriori Error Analysis for Evolution Nonlinear Schrödinger Equations up to the Critical Exponent ⋮ Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation ⋮ A posteriori error control and adaptivity for Crank-Nicolson finite element approximations for the linear Schrödinger equation ⋮ A posteriori error estimates for the Crank–Nicolson method for parabolic equations ⋮ Convergence analysis of the localized orthogonal decomposition method for the semiclassical Schrödinger equations with multiscale potentials

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