Cauchy problems with periodic controls.
Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
Compactness methods for quasi-linear evolution-equations
Comparison of exact and approximate causal solutions of a model curved-space wave equation
Compatible discretization of second-order elliptic problems.
Comportements limites des solutions de certains problèmes mixtes pour des équations paraboliques et leurs applications
Contingent solutions to the center manifold equation
Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies
In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...
Convergence analysis of finite difference schemes for semi-linear initial-value problems
Convergence dans de la solution de l’équation de Klein-Gordon vers celle de l’équation des ondes
Convergence of a difference method for a system of first order partial differential equations of hyperbolic type
Convergence of a finite element method based on the dual variational formulation
Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...
Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...
Convergence of iterative methods applied to generalized Fisher equation.
Convergence results for unbounded solutions of first order non-linear differential-functional equations
We consider the Cauchy problem in an unbounded region for equations of the type either or . We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Curved triangular finite -elements
Curved triangular -elements which can be pieced together with the generalized Bell’s -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the...