Analysis of new augmented Lagrangian formulations for mixed finite element schemes
type: Item
instance of: scholarly article
title: Analysis of new augmented Lagrangian formulations for mixed finite element schemes
zbMATH Open document ID: 0874.65085
author: Daniele Boffi
author: Carlo Lovadina
published in: Numerische Mathematik
publication date: 1997-06-30T00:00:00Z
review text: The authors analyse new augmented Lagrangian formulations for mixed finite element schemes which are useful to solve classical problems like the Stokes problem, the Laplace equation, the Reissner-Mindlin plate and shell problems. Such formulations are used to approximate solutions of minimization problems like: find \(u\) minimizing the functional \[ F(v)= {\textstyle {\frac12}} a(v,v)-\langle f,v\rangle \] under the linear constraint \(Lu=0\). They consist of -- introducing a Lagrange multiplier \(\mu\) and on approximating the saddle-point \((u,\lambda)\) of the functional \[ G(v,\mu)= F(v)+\langle Lv,\mu\rangle; \] -- replacing \(F\) by \(\widetilde{F}\), i.e., \[ \widetilde{F}(v)= F(v)+ {\textstyle {\frac\gamma2}}|Lv|^2, \] in order to prevent spurious modes. The present contribution concerns the analysis of the augmented Lagrangian method when the parameter \(\gamma\) depends on a power of the mesh-size \(h\). It is proved that such a dependency involves in some cases an improvement of the error estimates.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 1027742
zbMATH Keywords: mixed finite elements
zbMATH Keywords: augmented Lagrangian formulations
zbMATH Keywords: Stokes problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: Reissner-Mindlin plates
zbMATH Keywords: shell problems
zbMATH Keywords: error estimates
reviewed by: Michel Bernadou
MaRDI profile type: Publication
full work available at URL: s002110050246
OpenAlex ID: W2082353735
DOI: 10.1007/S002110050246
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description: scientific article; zbMATH DE number 1027742