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An analysis technique for stabilized finite element solution of incompressible flows

Tomás Chacón Rebollo (2001)

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

This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the stability of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.

An analysis technique for stabilized finite element solution of incompressible flows

Tomás Chacón Rebollo (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper presents an extension to stabilized methods of the standard technique for the numerical analysis of mixed methods. We prove that the stability of stabilized methods follows from an underlying discrete inf-sup condition, plus a uniform separation property between bubble and velocity finite element spaces. We apply the technique introduced to prove the sta bi li ty of stabilized spectral element methods so as stabilized solution of the primitive equations of the ocean.

An analytic proof of numerical stability of Gaussian collocation for delay differential

Nicola Guglielmi (2000)

Bollettino dell'Unione Matematica Italiana

In questo articolo si investigano le proprietà di stabilità asintotica dei metodi numerici per equazioni differenziali con ritardo, prendendo in esame l'equazione test: U t = a U t + b U t - τ dove a , b R , τ > 0 e g t è una funzione a valori reali e continua. In particolare, viene analizzata la dipendenza dal ritardo della stabilità numerica dei metodi di collocazione Gaussiana. Nel recente lavoro [GH99], la stabilità di questi metodi è stata dimostrata facendo uso di un approccio geometrico, basato sul legame tra la proprietà...

An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

Mikaël Barboteu, Krzysztof Bartosz, Piotr Kalita (2013)

International Journal of Applied Mathematics and Computer Science

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach...

An application of the BDDC method to the Navier-Stokes equations in 3-D cavity

Hanek, Martin, Šístek, Jakub, Burda, Pavel (2015)

Programs and Algorithms of Numerical Mathematics

We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab)...

An application of the induction method of V. Pták to the study of regula falsi

Florian-Alexandru Potra (1981)

Aplikace matematiky

In this paper we introduce the notion of " p -dimensional rate of convergence" which generalizes the notion of rate of convergence introduced by V. Pták. Using this notion we give a generalization of the Induction Theorem of V. Pták, which may constitute a basis for the study of the iterative procedures of the form X n + 1 = F ( x n - p + 1 , X n - p + 2 , ... , x n ) , n = 0 , 1 , 2 , ... . As an illustration we apply these results to the study of the convergence of the secant method, obtaining sharp estimates for the errors at each step of the iterative procedure.

An approach to robust network design in telecommunications

Georgios Petrou, Claude Lemaréchal, Adam Ouorou (2007)

RAIRO - Operations Research

In telecommunications network design, one of the most frequent problems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, these requirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technology development and customer movement due to competitiveness, the demands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a major consideration....

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