Nitsche's Method for Kirchhoff Plates

DOI10.1137/20M1349801zbMath1471.65195arXiv2007.00403OpenAlexW3160153167MaRDI QIDQ4997371

Juha H. Videman, Tom Gustafsson, Rolf Stenberg

Publication date: 29 June 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00403

zbMATH Keywords

finite elementsKirchhoff plateNitsche's method

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

kirchhoff-nitsche-ex1 ⋮ kirchhoff-nitsche-ex2 ⋮ kirchhoff-nitsche-ex3

Uses Software

• Matlab
• Getfem++
• Algorithm 884
• scikit-fem

Cites Work

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• A family of \(C^{0}\) finite elements for Kirchhoff plates. II: Numerical results
• An improved a priori error analysis of Nitsche's method for Robin boundary conditions
• Isoparametric \(C ^{0}\) interior penalty methods for plate bending problems on smooth domains
• Accurate bending analysis of rectangular thin plates with corner supports by a unified finite integral transform method
• 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)
• Nitsche’s method for general boundary conditions
• A Family of ${C}^0$ Finite Elements For Kirchhoff Plates I: Error Analysis
• A Posteriori Estimates for Conforming Kirchhoff Plate Elements
• GetFEM
• The Hellan--Herrmann--Johnson Method with Curved Elements