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3 results on '"Laboratoire Européen Associé CNRS Franco-Roumain de Mathématiques et Modélisation LEA Math-Mode"'

1. A class of dynamic contact problems with Coulomb friction in viscoelasticity

Author

Marius Cocou, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Européen Associé CNRS Franco-Roumain de Mathématiques et Modélisation LEA Math-Mode, and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)

Subjects
Surface (mathematics), Work (thermodynamics), set-valued mapping, Fixed-point theorem, Unilateral contact, MSC(2010): 35Q74, 49J40, 74A55, 74D05, 74H20, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Type (model theory), 01 natural sciences, Viscoelasticity, Dynamic problem, pointwise conditions, 0101 mathematics, viscoelasticity, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, General Engineering, General Medicine, 010101 applied mathematics, Computational Mathematics, Coulomb friction, Classical mechanics, Compact space, Dynamic problems, General Economics, Econometrics and Finance, Analysis
Abstract

International audience; The aim of this work is to study a class of nonsmooth dynamic contact problem which model several surface interactions, including relaxed unilateral contact conditions, adhesion and Coulomb friction laws, between two viscoelastic bodies of Kelvin-Voigt type. An abstract formulation which generalizes these problems is considered and the existence of a solution is proved by using Ky Fan's fixed point theorem, suitable approximation properties, several estimates and compactness arguments.

Published
2015
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2. Internal and subspace correction approximations of implicit variational inequalities

Author

Lori Badea, Marius Cocou, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Européen Associé CNRS Franco-Roumain de Mathématiques et Modélisation LEA Math-Mode, and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)

Subjects
Continuous solution, Approximations of π, General Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], 01 natural sciences, 010101 applied mathematics, Correction algorithm, Mechanics of Materials, Variational inequality, General Materials Science, 0101 mathematics, Elasticity (economics), Subspace topology, Quasistatic process, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

International audience; The aim of this paper is to study the existence of solutions and some approximations for a class of implicit evolution variational inequalities that represents a generalization of several quasistatic contact problems in elasticity. Using appropriate estimates for the incremental solutions, the existence of a continuous solution and convergence results are proved for some corresponding internal approximation and backward difference scheme. To solve the fully discrete problems, general additive subspace correction algorithms are considered, for which global convergence is proved and some error estimates are established.

Published
2015
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3. Approximation results and subspace correction algorithms for implicit variational inequalities

Author

Lori Badea, Marius Cocou, 'Simion Stoilow' Institute of Mathematics (IMAR), Romanian Academy of Sciences, Matériaux et Structures (M&S), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Européen Associé CNRS Franco-Roumain de Mathématiques et Modélisation LEA Math-Mode, and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)

Subjects
Class (set theory), implicit variational inequalities, Discretization, approximation and existence results, 010103 numerical & computational mathematics, Schwarz method, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], 01 natural sciences, Convergence (routing), Discrete Mathematics and Combinatorics, Applied mathematics, 0101 mathematics, Mathematics, Applied Mathematics, Mathematical analysis, multilevel methods, Domain decomposition methods, subspace correction, Elasticity (physics), 010101 applied mathematics, domain decomposition, Evolution problems, Variational inequality, Analysis, Quasistatic process, Subspace topology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; This paper deals with the mathematical analysis and the subspace approximation of a system of variational inequalities representing a unified approach to several quasistatic contact problems in elasticity. Using an implicit time discretization scheme and some estimates, convergence properties of the incremental solutions and existence results are presented for a class of abstract implicit evolution variational inequalities involving a nonlinear operator. To solve the corresponding semi-discrete and the fully discrete problems, some general subspace correction algorithms are proposed, for which global convergence is analyzed and error estimates are established.

Published
2013
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