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Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm
Mathematics, University College London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Mathematics and Mathematical Statistics, Umeå University, Sweden.
Mathematics and Mathematical Statistics, Umeå University, Sweden.
2023 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 417, no Part B, article id 116302Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 417, no Part B, article id 116302
Keywords [en]
Dual norm residual minimization, Error estimates, Finite element method, Galerkin Least Squares, Isogeometric analysis, Computation theory, Constrained optimization, Galerkin methods, Lagrange multipliers, Least squares approximations, Augmented Lagrangians, Lagrangian techniques, Least-squares- methods, Nonstandard problems, Residual minimization, Stability theories
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-62510DOI: 10.1016/j.cma.2023.116302ISI: 001114119400001Scopus ID: 2-s2.0-85169927833Local ID: ;intsam;62510OAI: oai:DiVA.org:hj-62510DiVA, id: diva2:1798783
Funder
Swedish Research Council, 2021-04925, 2022-03908eSSENCE - An eScience Collaboration, EP/T033126/1, EP/V050400/1Available from: 2023-09-20 Created: 2023-09-20 Last updated: 2024-01-09Bibliographically approved

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Hansbo, Peter

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