Displaying similar documents to “Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case”

New mixed finite volume methods for second order eliptic problems

Kwang Y. Kim (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on (div)- approximations for the vector variable and approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over the mixed...

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based...

A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

Tomás P. Barrios, Gabriel N. Gatica, María González, Norbert Heuer (2006)

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

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In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize...

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into . We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete...

A posteriori error estimates for the 3 D stabilized Mortar finite element method applied to the Laplace equation

Zakaria Belhachmi (2003)

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

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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also...

A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media

María-Luisa Rapún, Francisco-Javier Sayas (2006)

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

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This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating...

Mixed formulations for a class of variational inequalities

Leila Slimane, Abderrahmane Bendali, Patrick Laborde (2004)

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

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A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed...

Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition

Eliane Bécache, Jeronimo Rodríguez, Chrysoula Tsogka (2009)

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

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The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is not...