Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: The primal–dual formulation and a posteriori error estimation

Dörsek, Philipp; Melenk, Jens Markus

doi:10.1016/j.apnum.2010.03.011

Cited by 20 publications

(17 citation statements)

References 33 publications

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“…[27,39]). In forthcoming studies may be considered the extension to the Coulomb friction problem, numerical experiments and a-posteriori error estimators (as in [14]). …”

Section: Discussionmentioning

confidence: 99%

An adaptation of Nitscheʼs method to the Tresca friction problem

Chouly

2014

Journal of Mathematical Analysis and Applications

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We propose a simple adaptation to the Tresca friction case of the Nitsche-based finite element method given in [Chouly-Hild, 2012, Chouly-Hild-Renard, 2013 ] for frictionless unilateral contact. Both cases of unilateral and bilateral contact with friction are taken into account, with emphasis on frictional unilateral contact for the numerical analysis. We manage to prove theoretically the fully optimal convergence rate of the method in the H 1 (Ω)-norm which is O(h +ν (Ω), 0 < ν ≤ 1/2, in two dimensions and three dimensions, for Lagrange piecewise linear and quadratic finite elements. No additional assumption on the friction set is needed to obtain this proof.

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“…[27,39]). In forthcoming studies may be considered the extension to the Coulomb friction problem, numerical experiments and a-posteriori error estimators (as in [14]). …”

Section: Discussionmentioning

confidence: 99%

An adaptation of Nitscheʼs method to the Tresca friction problem

Chouly

2014

Journal of Mathematical Analysis and Applications

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“…To include the sign condition, we enforce the discrete Lagrange multiplier to be positive only in Gauss quadrature points leading to a non-conforming discretization. This approach was already suggested in [4] for frictional contact problems. We show the convergence of the mixed scheme and discuss some arguments as proposed by Haslinger et al and Lhalouani et al, cf.…”

Section: Introductionmentioning

confidence: 92%

Mixed finite element methods for two-body contact problems

Schröder

Kleemann

Blum

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper presents mixed finite element methods of higher-order for two-body contact problems of linear elasticity. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. The main focus is on the convergence of the scheme and on a priori estimates for the h-and the p-method. For this purpose, a discrete inf-sup condition is proven which guarantees the stability of the mixed method. Numerical results confirm the theoretical findings.

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“…For constant ansatz functions we define C 0 := {0 d−1 }, whereas for q = 1 the set C 1 consists of the corners of the reference element [−1, 1] d−1 . The non-conforming ansatz was proposed in [36] and convergence is shown for an elastic two-body problem in [29]. In the case of lower polynomial degrees q = 0, 1, this ansatz becomes conforming, since the choice of C q leads to a uniform sign condition on the elements E ∈ B H .…”

Section: Discretizationmentioning

confidence: 99%

Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems

Blum

Frohne

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this article a semi-smooth Newton method for frictional two-body contact problems and a solution algorithm for the resulting sequence of linear systems are presented. It is based on a mixed variational formulation of the problem and a discretization by finite elements of higher-order. General friction laws depending on the normal stresses and elasto-plastic material behavior with linear isotropic hardening are considered. Numerical results show the efficiency of the presented algorithm.

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Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: The primal–dual formulation and a posteriori error estimation

Cited by 20 publications

References 33 publications

An adaptation of Nitscheʼs method to the Tresca friction problem

An adaptation of Nitscheʼs method to the Tresca friction problem

Mixed finite element methods for two-body contact problems

Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems

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