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Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

Aplikace matematiky

The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.

Finite element approximation of a contact vector eigenvalue problem

Hennie de Schepper, Roger Van Keer (2003)

Applications of Mathematics

We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error...

Finite element approximations for the stationary large eddy simulation model

Andrzej Warzyński (2010)

Applicationes Mathematicae

Some approximation procedures are presented for the system of equations arising from the large eddy simulation of turbulent flows. Existence of solutions to the approximate problems is proved. Discrete solutions generate a strongly convergent subsequence whose limit is a weak solution of the original problem. To prove the convergence theorem we use Young measures and related tools. We do not limit ourselves to divergence-free functions and our results are in particular valid for finite element approximations...

Finite element approximations of a glaciology problem

Sum S. Chow, Graham F. Carey, Michael L. Anderson (2004)

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

In this paper we study a model problem describing the movement of a glacier under Glen’s flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...

Finite element approximations of a glaciology problem

Sum S. Chow, Graham F. Carey, Michael L. Anderson (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a model problem describing the movement of a glacier under Glen's flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in [Colinge and...

Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.

Finite element approximations of the three dimensional Monge-Ampère equation

Susanne Cecelia Brenner, Michael Neilan (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.

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