Helge Holden, Xavier Raynaud (2008)
Annales de l’institut Fourier
We show that the periodic Camassa–Holm equation possesses a global continuous semigroup of weak conservative solutions for initial data in . The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure with . The total energy is preserved by the solution.
Angela Handlovičová (2007)
Kybernetika
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Dong, Hongjie, Krylov, Nicolai V. (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
J.M., Spijker, M.N. Sanz-Serna (1986)
Numerische Mathematik
Philippe Helluy, Nicolas Seguin (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
Crouzeix, Michel, Thomée, Vidar (2001)
Computational Methods in Applied Mathematics
Bakaev, Nikolai Yu. (2004)
International Journal of Mathematics and Mathematical Sciences
Shanghui Jia, Deli Li, Tang Liu, Shu Hua Zhang (2008)
Applications of Mathematics
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
M. Chakir, D. Ouazar, A. Taik (2009)
Mathematical Modelling of Natural Phenomena
The flow trough the Strait of Gibraltar could be analyzed as a problem of two-layer hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The shallow water equations in both layers coupled together are an important tool to simulate this phenomenon. In this paper we perform an upwind schemes for hyperbolic equations based on the Roe approximate Riemann solver, to study the resulting model. The main goal assigned was to predict the location of the interface between the two layers....
Merazga, Nabil, Bouziani, Abdelfatah (2003)
Abstract and Applied Analysis
R. Stankiewicz (1990)
Banach Center Publications
Marian Malec (1977)
Annales Polonici Mathematici
Christophe Berthon, Yves Coudière, Vivien Desveaux (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation...
L. A. Bales (1993)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Marie-Noëlle Le Roux (1979)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Jozef Kacur, Roger Van Keer (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Jozef Kacur, Roger Van Keer (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Jozef Kacur, Roger Van Keer (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard’s equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Jozef Kacur, Roger Van Keer (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Willi Jäger, Jozef Kacur (1991/1992)
Numerische Mathematik