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Uniformly exponentially stable approximations for a class of second order evolution equations

Karim Ramdani, Takéo Takahashi, Marius Tucsnak (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes

Friedhelm Schieweck (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous P r - 1 -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.

Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem

Stanislav Sysala (2008)

Applications of Mathematics

The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...

Unique solvability and stability analysis of a generalized particle method for a Poisson equation in discrete Sobolev norms

Yusuke Imoto (2019)

Applications of Mathematics

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...

Universality of the best determined terms method

Jiří Neuberg (1979)

Aplikace matematiky

The properties are studied of the best determined terms method with respect to an a priori decomposition R ( T ) . The universal approximation to the normal solution of the first kind Fredholm integral equation is found.

Universally optimal approximation of functionals

Milan Práger (1979)

Aplikace matematiky

A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.

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