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Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...

Mesh r-adaptation for unilateral contact problems

Pierre Béal, Jonas Koko, Rachid Touzani (2002)

International Journal of Applied Mathematics and Computer Science

We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method.

Mesh Refinement For Stabilized Convection Diffusion Equations

B. Achchab, M. El Fatini, A. Souissi (2010)

Mathematical Modelling of Natural Phenomena

We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local

Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition

Koya Sakakibara (2017)

Applications of Mathematics

The aim of this paper is to analyze mathematically the method of fundamental solutions applied to the biharmonic problem. The key idea is to use Almansi-type decomposition of biharmonic functions, which enables us to represent the biharmonic function in terms of two harmonic functions. Based on this decomposition, we prove that an approximate solution exists uniquely and that the approximation error decays exponentially with respect to the number of the singular points. We finally present results...

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

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

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.

Mixed approximation of eigenvalue problems: A superconvergence result

Francesca Gardini (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini...

Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case

Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau (2005)

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

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg. 191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...

Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp.22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg.191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...

Mixed finite element analysis of semi-coercive unilateral contact problems with given friction

Ivan Hlaváček (2007)

Applications of Mathematics

A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the algorithm of...

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