On Nitsche's Method for Elastic Contact Problems
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Publication:5221024
DOI10.1137/19M1246869zbMath1447.65143arXiv1902.09312OpenAlexW3013756537MaRDI QIDQ5221024
Juha H. Videman, Tom Gustafsson, Rolf Stenberg
Publication date: 27 March 2020
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.09312
Classical linear elasticity (74B05) Contact in solid mechanics (74M15) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs in connection with mechanics of deformable solids (35Q74)
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Cites Work
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- On the connection between the stabilized Lagrange multiplier and Nitsche's methods
- An introduction to Sobolev spaces and interpolation spaces
- Boundary Lagrange multipliers in finite element methods: Error analysis in natural norms
- The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition
- Solution of variational inequalities in mechanics
- An unbiased Nitsche's approximation of the frictional contact between two elastic structures
- On finite element formulations for the obstacle problem -- mixed and stabilised methods
- On some techniques for approximating boundary conditions in the finite element method
- Error analysis of Nitsche's mortar method
- An efficient and reliable residual-type a posteriori error estimator for the Signorini problem
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- The finite element method with Lagrangian multipliers
- An overview of recent results on Nitsche's method for contact problems
- A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis
- Variationally consistent discretization schemes and numerical algorithms for contact problems
- Mixed and Hybrid Finite Element Methods
- A finite element method for domain decomposition with non-matching grids
- Residual-based a posteriori error estimation for contact problems approximated by Nitsche’s method
- Mixed and Stabilized Finite Element Methods for the Obstacle Problem
- Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method
- An Optimal A Priori Error Estimate for Nonlinear Multibody Contact Problems
