Nitsche methods for constrained problems in mechanics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866917449707814912 |
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| author | Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha |
| author_facet | Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha |
| contents | We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element method for the saddle point formulation where a Lagrange multiplier enforces the underlying constraint. The Nitsche method is then presented in a general minimization form, suitable for adding constraints to nonlinear finite element methods and allowing straightforward computational implementation with automatic differentation. This extends the method beyond classical boundary condition enforcement. To validate these ideas, we present Nitsche formulations for a range of problems in solid mechanics and give numerical evidence of the convergence rates of the Nitsche method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nitsche methods for constrained problems in mechanics Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha Numerical Analysis 65N30, 74M15, 49J40 We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element method for the saddle point formulation where a Lagrange multiplier enforces the underlying constraint. The Nitsche method is then presented in a general minimization form, suitable for adding constraints to nonlinear finite element methods and allowing straightforward computational implementation with automatic differentation. This extends the method beyond classical boundary condition enforcement. To validate these ideas, we present Nitsche formulations for a range of problems in solid mechanics and give numerical evidence of the convergence rates of the Nitsche method. |
| title | Nitsche methods for constrained problems in mechanics |
| topic | Numerical Analysis 65N30, 74M15, 49J40 |
| url | https://arxiv.org/abs/2603.05008 |