Displaying similar documents to “Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian”

Error Control and Andaptivity for a Phase Relaxation Model

Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The phase relaxation model is a diffuse interface model with small parameter which consists of a parabolic PDE for temperature and an ODE with double obstacles for phase variable . To decouple the system a semi-explicit Euler method with variable step-size is used for time discretization, which requires the stability constraint . Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter are further employed for space discretization. error estimates...

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

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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 [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...

A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations

Christophe Prud'homme, Dimitrios V. Rovas, Karen Veroy, Anthony T. Patera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are () (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned by...

Symmetric parareal algorithms for hamiltonian systems

Xiaoying Dai, Claude Le Bris, Frédéric Legoll, Yvon Maday (2013)

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

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The parareal in time algorithm allows for efficient parallel numerical simulations of time-dependent problems. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available. In this article, we are concerned with the long time integration of Hamiltonian systems. Geometric, structure-preserving integrators...

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

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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 [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...