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Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case

Jean Luc Guermond, Peter D. Minev (2002)

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

We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.

Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case

Jean Luc Guermond, Peter D. Minev (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.

Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients

Zakaria Belhachmi, Christine Bernardi, Andreas Karageorghis (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.

Mortar spectral method in axisymmetric domains

Saloua Mani Aouadi, Jamil Satouri (2013)

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

We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.

Mortar spectral method in axisymmetric domains

Saloua Mani Aouadi, Jamil Satouri (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy...

New results concerning the DWR method for some nonconforming FEM

Reiner Vanselow (2012)

Applications of Mathematics

This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete H 1 -seminorm are derived.

Nonuniqueness for some linear oblique derivative problems for elliptic equations

Gary M. Lieberman (1999)

Commentationes Mathematicae Universitatis Carolinae

It is well-known that the “standard” oblique derivative problem, Δ u = 0 in Ω , ∂ u / ∂ ν - u = 0 on ∂ Ω ( ν is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simple examples to demonstrate what can happen.

Nouvelles formulations intégrales pour les problèmes de diffraction d’ondes

David P. Levadoux, Bastiaan L. Michielsen (2004)

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

We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....

Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes

David P. Levadoux, Bastiaan L. Michielsen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2004)

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

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace’s equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Numerical analysis of the MFS for certain harmonic problems

Yiorgos-Sokratis Smyrlis, Andreas Karageorghis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace's equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...

Currently displaying 281 – 300 of 664