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A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, Gabriel Turinici (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...

A priori convergence of the Greedy algorithm for the parametrized reduced basis method

Annalisa Buffa, Yvon Maday, Anthony T. Patera, Christophe Prud’homme, Gabriel Turinici (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the a priori convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we...

A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem

Carolina Domínguez, Gabriel N. Gatica, Salim Meddahi, Ricardo Oyarzúa (2013)

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

We introduce and analyze a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The model consists of an elastic body which is subject to a given incident wave that travels in the fluid surrounding it. Actually, the fluid is supposed to occupy an annular region, and hence a Robin boundary condition imitating the behavior of the scattered field at infinity is imposed on its exterior boundary, which is located far from the obstacle. The media are governed by the elastodynamic...

A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D

Bishnu P. Lamichhane, Barbara I. Wohlmuth (2004)

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

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers as...

A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D

Bishnu P. Lamichhane, Barbara I. Wohlmuth (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative solvers...

A reduced basis element method for the steady Stokes problem

Alf Emil Løvgren, Yvon Maday, Einar M. Rønquist (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into a series of subdomains that are deformations of a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same...

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

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 the singularities...

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 (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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 the singularities...

A second-order finite volume element method on quadrilateral meshes for elliptic equations

Min Yang (2006)

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

In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H 1 -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.

A second-order finite volume element method on quadrilateral meshes for elliptic equations

Min Yang (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

Annalisa Buffa, Yvon Maday, Francesca Rapetti (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...

A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines

Annalisa Buffa, Yvon Maday, Francesca Rapetti (2001)

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

The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...

A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

Dinh Bao Phuong Huynh, David J. Knezevic, Anthony T. Patera (2013)

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

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port”...

A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces...

Currently displaying 81 – 100 of 156