A. Agouzal - Academia.edu (original) (raw)
Papers by A. Agouzal
Journal of Scientific Computing, 2013
L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » (http:/... more L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » (http://www.esaim-m2an.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/
Mathematical Modelling of Natural Phenomena, 2010
We present a new method for generating a d-dimensional simplicial mesh that minimizes the L p-nor... more We present a new method for generating a d-dimensional simplicial mesh that minimizes the L p-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method.
Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010
Numerical solution of partial differential equations requires appropriate meshes, efficient solve... more Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh
Proceedings of the 18th International Meshing Roundtable, 2009
ABSTRACT We present a new technology for generating meshes minimizing the interpolation and discr... more ABSTRACT We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N h triangles, the error is proportional to Nh-1N_h^{-1} and the gradient of error is proportional to Nh-1/2N_h^{-1/2} which are the optimal asymptotics. The methodology is verified with numerical experiments.
Proceedings of the 16th International Meshing Roundtable, 2008
We study methods for recovering tensor metrics from given error estimates and properties of meshe... more We study methods for recovering tensor metrics from given error estimates and properties of meshes which are quasi-uniform in these metrics. We derive optimal upper and lower bounds for the global error on these meshes. We demonstrate with numerical experiments that the edge-based error estimates are preferable for recovering anisotropic metrics than the conventional element-based errors estimates.
Numerical Methods for Partial Differential Equations, 2012
ABSTRACT We construct a hierarchical a posteriori error estimator for a stabilized finite element... more ABSTRACT We construct a hierarchical a posteriori error estimator for a stabilized finite element discretization of convection‐diffusion equations with height Péclet number. The error estimator is derived without the saturation assumption and without any comparison with the classical residual estimator. Besides, it is robust, such that the equivalence between the norm of the exact error and the error estimator is independent of the meshsize or the diffusivity parameter. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012
Russian Journal of Numerical Analysis and Mathematical Modelling, 2000
... Then, solution to the minimization problem (5) is MO ≡ YT o Yo = 1 √ μ2 − λ2 YT [ μ −λ −λ μ ]... more ... Then, solution to the minimization problem (5) is MO ≡ YT o Yo = 1 √ μ2 − λ2 YT [ μ −λ −λ μ ] Y, (6) where μ = 3 ∑ k=1 (Yek, Yek), λ = 3 ∑ k=1 (RYek, Yek), (7) R = [ 0 1 1 0 ] . Proof. Using Lemma 1, we obtain the following representation of matrix ˜Y T ˜Y: ...
Numerische Mathematik, 1998
We propose a generalisation of the hierarchical a posteriori error estimator of Bank-Weiser to mi... more We propose a generalisation of the hierarchical a posteriori error estimator of Bank-Weiser to mixed formulations, in the cases of conforming and non conforming approximations, with or without numerical integration. We present as examples of application: the Dirichlet problem for the Laplace operator, in mixed dual formulation, with and without numerical integration. Résumé. On propose une généralisation de l'estimateur a posteriori hiérarchique de Bank-Weiser aux formulation mixtes, dans le cas d'approximations conformes et non conformes, avec ou sans intégration numérique. On présente comme exemples d'application: la formulation mixte duale du problème de Dirichlet pour le Laplacien, avec et sans intégration numérique.
Numerical Methods for Partial Differential Equations, 2004
Page 1. Some Remarks about the Hierarchical A Posteriori Error Estimate B. Achchab,1 S. Achchab,2... more Page 1. Some Remarks about the Hierarchical A Posteriori Error Estimate B. Achchab,1 S. Achchab,2 A. Agouzal3 1Universite´ Hassan 1er, Faculte´ des sciences e´conomiques, BP 784 Settat, Morocco 2LERMA, Ecole Mohammadia d'Inge´nieurs, Avenue Ibn Sina. ...
Mathematical Modelling of Natural Phenomena, 2010
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are conside... more Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of IR d , d ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh.
Mathematical Modelling of Natural Phenomena, 2010
In this paper, a new a posteriori error estimator for nonconforming convection diffusion approxim... more In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimator.
Mathematical Methods in the Applied Sciences, 2003
This paper deals with numerical analysis of system coupling Navier-Stokes equations with two nonl... more This paper deals with numerical analysis of system coupling Navier-Stokes equations with two nonlinear reaction-di usion equations. This system modelize a propagation of reaction front at the case of polymerization. A ÿnite elements approximation is presented, the existence and uniqueness are established. Optimal error estimates are given. Copyright ? 2003 John Wiley & Sons, Ltd.
Journal of Numerical Mathematics, 2000
A new technique for the implementation of cell-centered finite volume schemes is proposed. It is ... more A new technique for the implementation of cell-centered finite volume schemes is proposed. It is based on an equivalence between these schemes and the non-conforming Crouzeix-Raviart finite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two significant advantages that make it attractive. On the one hand the resulting formulation is well-defined on general unstructured meshes, with no restriction on (or ad-hoc treatment of) obtuse angles. On the other hand, it automatically provides a very effective, asymptotically exact, error estimator. An adaptive finite volume method, based on this estimator, is proposed and tested. It turns out to be remarkable for its exactness, even in coarse meshes.
Journal of Numerical Mathematics, 2000
Communications in Numerical Methods in Engineering, 1997
ABSTRACT
IMA Journal of Numerical Analysis, 2012
We consider a recently proposed finite-element space that consists of piecewise affine functions ... more We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming P 1 space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in W 1, p (Ω \ Γ) ∩ W 2,s (Ω \ Γ), the interpolant I h u defined by this new space satisfies u − I h u L q (Ω) C h 1+ 1 q − 1 p |u| W 1, p (Ω\Γ) + h 2 |u| W 2,s (Ω\Γ) , where h is the mesh size, Ω ⊂ R d is the domain, p > d, p q, s q and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finiteelement space as compared to any space consisting of functions that are continuous across Γ , which would yield an error in the L q (Ω)-norm of order h 1 q − 1 p. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.
ESAIM: Mathematical Modelling and Numerical Analysis, 1999
L'accès aux archives de la revue « ESAIM: Modélisation mathématique et analyse numérique » (http:... more L'accès aux archives de la revue « ESAIM: Modélisation mathématique et analyse numérique » (http://www.esaim-m2an.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Mathematical Modelling and Numerical Analysis
Journal of Scientific Computing, 2013
L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » (http:/... more L'accès aux archives de la revue « RAIRO-Modélisation mathématique et analyse numérique » (http://www.esaim-m2an.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/
Mathematical Modelling of Natural Phenomena, 2010
We present a new method for generating a d-dimensional simplicial mesh that minimizes the L p-nor... more We present a new method for generating a d-dimensional simplicial mesh that minimizes the L p-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method.
Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010
Numerical solution of partial differential equations requires appropriate meshes, efficient solve... more Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh
Proceedings of the 18th International Meshing Roundtable, 2009
ABSTRACT We present a new technology for generating meshes minimizing the interpolation and discr... more ABSTRACT We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N h triangles, the error is proportional to Nh-1N_h^{-1} and the gradient of error is proportional to Nh-1/2N_h^{-1/2} which are the optimal asymptotics. The methodology is verified with numerical experiments.
Proceedings of the 16th International Meshing Roundtable, 2008
We study methods for recovering tensor metrics from given error estimates and properties of meshe... more We study methods for recovering tensor metrics from given error estimates and properties of meshes which are quasi-uniform in these metrics. We derive optimal upper and lower bounds for the global error on these meshes. We demonstrate with numerical experiments that the edge-based error estimates are preferable for recovering anisotropic metrics than the conventional element-based errors estimates.
Numerical Methods for Partial Differential Equations, 2012
ABSTRACT We construct a hierarchical a posteriori error estimator for a stabilized finite element... more ABSTRACT We construct a hierarchical a posteriori error estimator for a stabilized finite element discretization of convection‐diffusion equations with height Péclet number. The error estimator is derived without the saturation assumption and without any comparison with the classical residual estimator. Besides, it is robust, such that the equivalence between the norm of the exact error and the error estimator is independent of the meshsize or the diffusivity parameter. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012
Russian Journal of Numerical Analysis and Mathematical Modelling, 2000
... Then, solution to the minimization problem (5) is MO ≡ YT o Yo = 1 √ μ2 − λ2 YT [ μ −λ −λ μ ]... more ... Then, solution to the minimization problem (5) is MO ≡ YT o Yo = 1 √ μ2 − λ2 YT [ μ −λ −λ μ ] Y, (6) where μ = 3 ∑ k=1 (Yek, Yek), λ = 3 ∑ k=1 (RYek, Yek), (7) R = [ 0 1 1 0 ] . Proof. Using Lemma 1, we obtain the following representation of matrix ˜Y T ˜Y: ...
Numerische Mathematik, 1998
We propose a generalisation of the hierarchical a posteriori error estimator of Bank-Weiser to mi... more We propose a generalisation of the hierarchical a posteriori error estimator of Bank-Weiser to mixed formulations, in the cases of conforming and non conforming approximations, with or without numerical integration. We present as examples of application: the Dirichlet problem for the Laplace operator, in mixed dual formulation, with and without numerical integration. Résumé. On propose une généralisation de l'estimateur a posteriori hiérarchique de Bank-Weiser aux formulation mixtes, dans le cas d'approximations conformes et non conformes, avec ou sans intégration numérique. On présente comme exemples d'application: la formulation mixte duale du problème de Dirichlet pour le Laplacien, avec et sans intégration numérique.
Numerical Methods for Partial Differential Equations, 2004
Page 1. Some Remarks about the Hierarchical A Posteriori Error Estimate B. Achchab,1 S. Achchab,2... more Page 1. Some Remarks about the Hierarchical A Posteriori Error Estimate B. Achchab,1 S. Achchab,2 A. Agouzal3 1Universite´ Hassan 1er, Faculte´ des sciences e´conomiques, BP 784 Settat, Morocco 2LERMA, Ecole Mohammadia d'Inge´nieurs, Avenue Ibn Sina. ...
Mathematical Modelling of Natural Phenomena, 2010
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are conside... more Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of IR d , d ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh.
Mathematical Modelling of Natural Phenomena, 2010
In this paper, a new a posteriori error estimator for nonconforming convection diffusion approxim... more In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimator.
Mathematical Methods in the Applied Sciences, 2003
This paper deals with numerical analysis of system coupling Navier-Stokes equations with two nonl... more This paper deals with numerical analysis of system coupling Navier-Stokes equations with two nonlinear reaction-di usion equations. This system modelize a propagation of reaction front at the case of polymerization. A ÿnite elements approximation is presented, the existence and uniqueness are established. Optimal error estimates are given. Copyright ? 2003 John Wiley & Sons, Ltd.
Journal of Numerical Mathematics, 2000
A new technique for the implementation of cell-centered finite volume schemes is proposed. It is ... more A new technique for the implementation of cell-centered finite volume schemes is proposed. It is based on an equivalence between these schemes and the non-conforming Crouzeix-Raviart finite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two significant advantages that make it attractive. On the one hand the resulting formulation is well-defined on general unstructured meshes, with no restriction on (or ad-hoc treatment of) obtuse angles. On the other hand, it automatically provides a very effective, asymptotically exact, error estimator. An adaptive finite volume method, based on this estimator, is proposed and tested. It turns out to be remarkable for its exactness, even in coarse meshes.
Journal of Numerical Mathematics, 2000
Communications in Numerical Methods in Engineering, 1997
ABSTRACT
IMA Journal of Numerical Analysis, 2012
We consider a recently proposed finite-element space that consists of piecewise affine functions ... more We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming P 1 space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in W 1, p (Ω \ Γ) ∩ W 2,s (Ω \ Γ), the interpolant I h u defined by this new space satisfies u − I h u L q (Ω) C h 1+ 1 q − 1 p |u| W 1, p (Ω\Γ) + h 2 |u| W 2,s (Ω\Γ) , where h is the mesh size, Ω ⊂ R d is the domain, p > d, p q, s q and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finiteelement space as compared to any space consisting of functions that are continuous across Γ , which would yield an error in the L q (Ω)-norm of order h 1 q − 1 p. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.
ESAIM: Mathematical Modelling and Numerical Analysis, 1999
L'accès aux archives de la revue « ESAIM: Modélisation mathématique et analyse numérique » (http:... more L'accès aux archives de la revue « ESAIM: Modélisation mathématique et analyse numérique » (http://www.esaim-m2an.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Mathematical Modelling and Numerical Analysis