On the convergence of a linear two-step finite element method
for the nonlinear Schrödinger equation

Georgios E. Zouraris

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Displaying similar documents to “On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation”

Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics

Othmar Koch, Christof Neuhauser, Mechthild Thalhammer (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order applied to the multi-configuration...

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

Thorsten Rohwedder (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the . Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis to obtain existence and uniqueness...

error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...

A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...