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

2022/07/01 by Erik Burman, Burman, Erik, Peter Hansbo +3 · 4 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2207.00294

openalex publication_date 2022/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A variational multiscale approach to PDE-constrained optimization problems arising in Data-Driven Computational Mechanics
• Iterative Contact-resolving Hybrid Methods for Multiscale Contact Mechanics
• Exact penalty functions and global saddle points of augmented Lagrangians for well-posed constrained optimization problems
• Numerical approximation of a PDE-constrained Optimization problem that appears in Data-Driven Computational Mechanics

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