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Claudio Padra

Bio: Claudio Padra is an academic researcher from Balseiro Institute. The author has contributed to research in topics: Finite element method & Estimator. The author has an hindex of 17, co-authored 26 publications receiving 1275 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the authors proposed an alternative way to compute the topological derivative based on the shape sensitivity analysis concepts, which leads to a more simple and constructive formulation than the ones found in the literature.

305 citations

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TL;DR: In this article, the authors introduce deux estimateurs d'erreur a posteriori for approximation par une methode d'elements finis non conforme d'un probleme elliptique du second ordre.
Abstract: On introduit deux «estimateurs» d'erreur a posteriori pour une approximation par une methode d'elements finis non conforme d'un probleme elliptique du second ordre On montre que ces «estimateurs» sont equivalents a la norme d'energie de l'erreur Finalement, on presente diverses experiences numeriques montrant le bon comportement de ces estimateurs, lorsqu'on les utilise comme indicateurs locaux d'erreurs pour un raffinement adaptatif

137 citations

Journal ArticleDOI
TL;DR: A simple proof of the equivalence, up to higher order terms, between the error and a residual type error estimator is given and it is proved that the volumetric part of the residual is dominated by a constant times the edge or face residuals.
Abstract: This paper deals with a posteriori error estimators for the linear finite element approximation of second-order elliptic eigenvalue problems in two or three dimensions. First, we give a simple proof of the equivalence, up to higher order terms, between the error and a residual type error estimator. Second, we prove that the volumetric part of the residual is dominated by a constant times the edge or face residuals, again up to higher order terms. This result was not known for eigenvalue problems.

129 citations

Journal ArticleDOI
TL;DR: In this article, the authors used the topological shape sensitivity method to obtain the topology derivative for three-dimensional linear elasticity problems, adopting the total potential energy as cost function and the equilibrium equation as constraint.

113 citations

Journal ArticleDOI
TL;DR: This paper defines and analyze a posteriori error estimators for nonconforming approximations of the Stokes equations and proves that these estimators are equivalent to an appropriate norm of the error.
Abstract: In this paper we define and analyze a posteriori error estimators for nonconforming approximations of the Stokes equations. We prove that these estimators are equivalent to an appropriate norm of the error. For the case of piecewise linear elements we define two estimators. Both of them are easy to compute, but the second is simpler because it can be computed using only the right-hand side and the approximate velocity. We show how the first estimator can be generalized to higher-order elements. Finally, we present several numerical examples in which one of our estimators is used for adaptive refinement.

108 citations


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Book
01 Jan 2000
TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
Abstract: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.

2,607 citations

Journal ArticleDOI
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Abstract: Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

1,816 citations

Journal ArticleDOI
TL;DR: The convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of thelevel-set function, hole nucleation and the relation of level-set methods to other topology optimization methods.
Abstract: This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.

716 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method.

517 citations