Georgios E. Zouraris (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the norm. We prove optimal order error estimates in the and norms, under mild mesh conditions for two and three space dimensions.
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...
Huirong Pi, Chunhua Wang (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer , there exists () > 0 such that, for 0 < < (), the problem has an -bump complex-valued solution. As a result, when → 0, the equation has more and more multi-bump complex-valued solutions.
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 ...
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 ( ...