Abstract:The theory behind Nitsche's method for approximating the obstacle problem of clamped Kirchhoff plates is reviewed. A priori estimates and residualbased a posteriori error estimators are presented for the related conforming stabilised finite element method and the latter are used for adaptive refinement in a numerical experiment.
“…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.…”
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.
“…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.…”
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.
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.
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