A Hybrid High-Order Discretization Combined with Nitsche's Method for Contact and Tresca Friction in Small Strain Elasticity
From MaRDI portal
Publication:5132032
DOI10.1137/19M1286499zbMath1452.65328MaRDI QIDQ5132032
Alexandre Ern, Nicolas Pignet, Franz Chouly
Publication date: 9 November 2020
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
elasticityunilateral contactNitsche's methodarbitrary orderTresca frictiongeneral mesheshybrid discretizationlocking-free methods
Contact in solid mechanics (74M15) Linear elasticity with initial stresses (74B10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method, Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem, Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting), Hybrid Discretizations in Solid Mechanics for Non-linear and Non-smooth Problems, Nitsche method for contact with Coulomb friction: existence results for the static and dynamic finite element formulations, BR2 discontinuous Galerkin methods for finite hyperelastic deformations, Discontinuous Galerkin methods for hemivariational inequalities in contact mechanics, Residual a posteriori error estimation for frictional contact with Nitsche method, Gradient recovery type a posteriori error estimates of virtual element method for an elliptic variational inequality of the second kind, A Polygonal Discontinuous Galerkin Formulation for Contact Mechanics in Fluid-Structure Interaction Problems, A unified framework for high-order numerical discretizations of variational inequalities, Convergence analysis of hybrid high-order methods for the wave equation, A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality, Stabilized finite elements for Tresca friction problem
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
- Mathematical aspects of discontinuous Galerkin methods.
- Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
- Hybrid high-order methods for finite deformations of hyperelastic materials
- An unbiased Nitsche's approximation of the frictional contact between two elastic structures
- A hybrid high-order locking-free method for linear elasticity on general meshes
- A virtual element method for contact
- On convergence of the penalty method for unilateral contact problems
- Weak-Galerkin finite element methods for a second-order elliptic variational inequality
- The local average contact (LAC) method
- A hybrid high-order method for incremental associative plasticity with small deformations
- Virtual element method for simplified friction problem
- An adaptation of Nitsche's method to the Tresca friction problem
- A posteriori error analysis for finite element solutions of a frictional contact problem
- Optimal convergence analysis of the unilateral contact problem with and without Tresca friction conditions by the penalty method
- Error analysis of HDG approximations for elliptic variational inequality: obstacle problem
- Équations et inéquations non linéaires dans les espaces vectoriels en dualité
- Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
- The nonconforming virtual element method
- A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis
- Discontinuous Galerkin methods for solving the Signorini problem
- Variationally consistent discretization schemes and numerical algorithms for contact problems
- Variational formulation of rate- and state-dependent friction problems
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Residual-based a posteriori error estimation for contact problems approximated by Nitsche’s method
- An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
- A Hybrid High-Order Method for Nonlinear Elasticity
- An Improved a Priori Error Analysis for Finite Element Approximations of Signorini's Problem
- Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: theory and numerical experiments
- Optimal Convergence for Discrete Variational Inequalities Modelling Signorini Contact in 2D and 3D without Additional Assumptions on the Unknown Contact Set
- Finite element quasi-interpolation and best approximation
- Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions