Burman, Erik;
Hansbo, Peter;
Larson, Mats G;
Larsson, Karl;
(2023)
Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm.
Computer Methods in Applied Mechanics and Engineering
, 417
(B)
, Article 116302. 10.1016/j.cma.2023.116302.
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Abstract
We explore how recent advances in Isogeometric analysis, Galerkin Least-Squares methods, and Augmented Lagrangian techniques can be applied to solve nonstandard problems, for which there is no classical stability theory, such as that provided by the Lax–Milgram lemma or the Banach-Necas-Babuska theorem. In particular, we consider continuation problems where a second-order partial differential equation with incomplete boundary data is solved given measurements of the solution on a subdomain of the computational domain. The use of higher regularity spline spaces leads to simplified formulations and potentially minimal multiplier space. We show that our formulation is inf-sup stable, and given appropriate a priori assumptions, we establish optimal order convergence.
| Type: | Article |
|---|---|
| Title: | Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2023.116302 |
| Publisher version: | https://doi.org/10.1016/j.cma.2023.116302 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| Keywords: | Finite element method, Isogeometric analysis, Galerkin Least Squares, Dual norm residual minimization, Error estimates |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10176584 |
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