Dense output for extrapolation methods.
E. Hairer, A. Ostermann (1990/91)
Numerische Mathematik
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E. Hairer, A. Ostermann (1990/91)
Numerische Mathematik
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Jun Lei, Pengbo Sun, Tinh Quoc Bui (2015)
Curved and Layered Structures
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To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack...
Guido Walz (1987)
Numerische Mathematik
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Franck Boyer, Sebastian Minjeaud (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated...
Reinhard Fößmeier (1987)
Numerische Mathematik
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Aurélie Edwards, Nicolas Seguin, Magali Tournus (2012)
ESAIM: Proceedings
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We present a finite volume type scheme to solve a transport nephron model. The model consists in a system of transport equations with specific boundary conditions. The transport velocity is driven by another equation that can undergo sign changes during the transient regime. This is the main difficulty for the numerical resolution. The scheme we propose is based on an explicit resolution and is stable under a CFL condition which does not depend on the stiffness of source terms. ...
Thierry Gallouët, Jean-Marc Hérard, Nicolas Seguin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure,...
Zahari Zlatev, István Faragó, Ágnes Havasi (2012)
Open Mathematics
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Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.