On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

Petr Harasim

Displaying similar documents to “On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients”

Finite element analysis of the Signorini problem

Jaroslav Haslinger (1979)

Commentationes Mathematicae Universitatis Carolinae

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On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation

Petr Harasim (2008)

Applications of Mathematics

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We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient. ...

Mixed formulation of elliptic variational inequalities and its approximation

Jaroslav Haslinger (1981)

Aplikace matematiky

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The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian $2$ on a certain convex set $K x Λ$ . Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.

Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and $L^{1}$ contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in $L^{1}$ and $L^{\infty}$ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive $L^{1}$ convergence without any convergence...