Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types.
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems.
Uniform stabilization of a viscous numerical approximation for a locally damped wave equation
This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the mesh size)...
Uniformly exponentially or polynomially stable approximations for second order evolution equations and some applications
In this paper, we consider the approximation of second order evolution equations. It is well known that the approximated system by finite element or finite difference is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial...
Uniformly exponentially stable approximations for a class of second order evolution equations
We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite difference are not, in general, uniformly stable with respect to the discretization parameter. Our main result shows that, by adding a suitable numerical viscosity term in the numerical scheme, our approximations are...
Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms
Unique solvability and stability analysis is conducted for a generalized particle method for a Poisson equation with a source term given in divergence form. The generalized particle method is a numerical method for partial differential equations categorized into meshfree particle methods and generally indicates conventional particle methods such as smoothed particle hydrodynamics and moving particle semi-implicit methods. Unique solvability is derived for the generalized particle method for the...
Variational data assimilation for discrete Burgers equation.
Vibrations of a beam between obstacles. Convergence of a fully discretized approximation
We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented....
Vorzeichenstabile Differenzenverfahren für parabolische Anfangsrandwertaufgaben.
Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
Задача Коши и смешанная задача для вырождающхся гиперболических уравнений второго порядка
Исследование разностных схем для квазилинейных вырождающихся параболических уравнений
Исследование сходимости разностных схем для многомерного вырождающегося параболического уравнения
Исследование сходимости разностных схем для одномерного вырождающегося параболического уравнения
Исследование устойчивости одной явной разностной схемы.
О корректности в сильной норме нелинейной двухслойной разностной схемы
О корректности нелинейной двухслойной разностной схемы с весами
О методах решения сеточных параболических задач, основанных на окаймлении матрицы
О некоторых результатах и проблемах теории устойчивости разностных схем
Об одном подходе к конструированию разностных схем для квазилинейных уравнений газовой динамики