On a class of implicit and explicit schemes of Van-Leer type for scalar conservation laws
On a diphasic low Mach number system
We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech. 42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...
On a diphasic low mach number system
We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...
On a Free Interface Problem for Linear Ordinary Differential Equations and the One-Phase Stefan Problem.
On a numerical approach to Stefan-like problems.
On error estimates in the Galerkin method for hyperbolic equations.
On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with...
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments...
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
On multigrid for linear complementarity problems with application to American-style options.
On multiresolution methods in numerical analysis.
On some finite difference schemes for solution of hyperbolic heat conduction problems
We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary value problem...
On stability of some difference schemes for parabolic diffusion equation.
On stability of spline difference scheme for reaction-diffusion time-dependent singularly perturbed problem.
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This...
On the approximation of front propagation problems with nonlocal terms
We investigate the approximation of the evolution of compact hypersurfaces of depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.
On the approximation of front propagation problems with nonlocal terms
We investigate the approximation of the evolution of compact hypersurfaces of depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.
On the approximation of the dynamics of sandpile surfaces.