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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Constrained optimization

Iterative methods

Lagrange multipliers

Augmented lagrange multiplier methods

Augmented Lagrangian methods

Constrained optimi-zation problems

Constraint equation

Galerkin Least Squares

Iterative algorithm

Lagrange multiplier method

Penalty term

Stabilization methods

Stabilized method

Computational mechanics

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