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Adaptive Quadratic Finite Element Method for the Unilateral Contact Problem
In this paper, we present and analyze a posteriori error estimates in the energy norm of a quadratic finite element method for the frictionless...
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On Numerical Solving of Junction Problem for the Thin Rigid and Elastic Inclusions in Elastic Body
AbstractWe consider a multiphysics problem of equilibrium for a two-dimensional elastic body containing a thin rigid and thin elastic inclusions. The...
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Aperiodical Isoperimetric Planar Homogenization with Critical Diameter: Universal Non-local Strange Term for a Dynamical Unilateral Boundary Condition
AbstractWe study the asymptotic behavior of the solution to the diffusion equation in a planar domain, perforated by tiny sets of different shapes...
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Nitsche’s Method
As we have seen in the previous Chap. 5 , it may not be the best idea to approximate directly...
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Tresca Friction
As a preliminary step before going into Coulomb friction, we focus on the numerical approximation of Tresca friction in this chapter. The Signorini...
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Splitting Method for the Variational Phase Transition Problem in Two-Phase Continuum Media
For the multi-dimensional variational phase transition problem of continuum mechanics we propose a method for splitting the problem into two parts...
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Existence and Convergence Results for an Elastic Frictional Contact Problem with Nonmonotone Subdifferential Boundary Conditions
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary...
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Contact Between Two Elastic Bodies
In this chapter, we detail the formulation for the contact between two elastic bodies, in the small deformation framework. This is mostly a...
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A Dual Method for Solving an Equilibrium Problem of a Body Containing a Thin Defect
AbstractAn equilibrium problem of a two-dimensional body with a thin defect whose properties are characterized by a fracture parameter is considered....
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Finite Element Approximation of Contact and Friction in Elasticity
This book presents the mathematics behind the formulation, approximation, and numerical analysis of contact and friction problems. It also provides a...
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A Fully-Discrete Finite Element Scheme and Projection-Iteration Algorithm for a Dynamic Contact Problem with Multi-contact Zones and Unilateral Constraint
A fully discrete finite element scheme is proposed to solve the dynamic viscoelastic contact problem with multi-contact zones and unilateral...
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Unexpected regionally negative solutions of the homogenization of Poisson equation with dynamic unilateral boundary conditions: critical symmetric particles
We obtain the homogenized problem associated with the Poisson equation in a domain perforated by "tiny" balls (or in a domain defined as the exterior...
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Local Flux Reconstruction for a Frictionless Unilateral Contact Problem
We are interested in the a posteriori error analysis based on locally reconstructed fluxes for the 2D Signorini problem. We start from a...
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A modified inertial Tseng technique of Bilevel variational inequality problem with application to image processing
In this paper, we propose and study a new modified Tseng inertial iterative technique for solving Bilevel quasimonotone Variational Inequality...
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On Implementing Boundary Conditions for a Rate-Form Quasi-Static Contact Problem with Friction: A Node-to-Facet Finite Element Approach
AbstractA quasi-static geometrically non-linear initial-boundary value problem is considered in a rate form for investigating deformation of a solid....
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Numerical Approximation of the Solution of an Obstacle Problem Modelling the Displacement of Elliptic Membrane Shells via the Penalty Method
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the...
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A priori error analysis of virtual element method for contact problem
As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for...
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Contact and Self-contact in Large Strain
In many engineering applications, the elastic bodies in contact may undergo large transformations. In this case, a setting such as presented in Chap....