Nitsche’s Method for the Obstacle Problem of Clamped Kirchhoff Plates

Gustafsson, Tom; Stenberg, Rolf; Videman, Juha H.

doi:10.1007/978-3-319-96415-7_36

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The Plate Obstacle Problem1

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2022

2023

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“…with γ 1 a sufficiently large constant. A similar approach has been suggested by Gustafsson et al [61,62] in the context of C 1 approximations of the clamped Kirchhoff plate with GLS stabilisation, without specific reference to augmented Lagrangian methods.…”

Section: The Plate Obstacle Problemmentioning

confidence: 92%

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics

Burman¹,

Hansbo²,

Larson³

2022

Preprint

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In this paper we will review recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier-free stabilised methods. We first show how the method generates Galerkin/Least Squares type schemes for equality constraints and then how it can be extended to develop new stabilised methods for inequality constraints. Application to several different problems in computational mechanics is given.

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Section: The Plate Obstacle Problemmentioning

confidence: 92%

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics

Burman¹,

Hansbo²,

Larson³

2022

Preprint

View full text Add to dashboard Cite

show abstract

The Augmented Lagrangian Method as a Framework for Stabilised Methods in Computational Mechanics

Burman

Hansbo

Larson

2023

Arch Computat Methods Eng

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In this paper we will present a review of recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier-free stabilised methods. The augmented Lagrangian method consists of a standard Lagrange multiplier method augmented by a penalty term, penalising the constraint equations, and is well known as the basis for iterative algorithms for constrained optimisation problems. Its use as a stabilisation methods in computational mechanics has, however, only recently been appreciated. We first show how the method generates Galerkin/Least Squares type schemes for equality constraints and then how it can be extended to develop new stabilised methods for inequality constraints. Application to several different problems in computational mechanics is given.

show abstract

Nitsche’s Method for the Obstacle Problem of Clamped Kirchhoff Plates

Cited by 2 publications

References 24 publications

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics

The augmented Lagrangian method as a framework for stabilised methods in computational mechanics

The Augmented Lagrangian Method as a Framework for Stabilised Methods in Computational Mechanics

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