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

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