On the spectrum of the finite element approximation of a three field formulation for linear elasticity
We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-11-01
|
| Series: | Examples and Counterexamples |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X22000155 |
| _version_ | 1811294141256040448 |
|---|---|
| author | Linda Alzaben Fleurianne Bertrand Daniele Boffi |
| author_facet | Linda Alzaben Fleurianne Bertrand Daniele Boffi |
| author_sort | Linda Alzaben |
| collection | DOAJ |
| description | We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit. |
| first_indexed | 2024-04-13T05:12:12Z |
| format | Article |
| id | doaj.art-8d73a5c6240145d2a154ade76a670ab5 |
| institution | Directory Open Access Journal |
| issn | 2666-657X |
| language | English |
| last_indexed | 2024-04-13T05:12:12Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj.art-8d73a5c6240145d2a154ade76a670ab52022-12-22T03:01:00ZengElsevierExamples and Counterexamples2666-657X2022-11-012100076On the spectrum of the finite element approximation of a three field formulation for linear elasticityLinda Alzaben0Fleurianne Bertrand1Daniele Boffi2Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi ArabiaFaculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, 7500, The NetherlandsComputer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia; Dipartimento di Matematica “F. Casorati”, University of Pavia, Via Ferrata 1, Pavia, I-27100, Italy; Corresponding author at: Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia.We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.http://www.sciencedirect.com/science/article/pii/S2666657X22000155Eigenvalue problemLinear elasticityLeast-squares finite elements |
| spellingShingle | Linda Alzaben Fleurianne Bertrand Daniele Boffi On the spectrum of the finite element approximation of a three field formulation for linear elasticity Examples and Counterexamples Eigenvalue problem Linear elasticity Least-squares finite elements |
| title | On the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| title_full | On the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| title_fullStr | On the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| title_full_unstemmed | On the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| title_short | On the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| title_sort | on the spectrum of the finite element approximation of a three field formulation for linear elasticity |
| topic | Eigenvalue problem Linear elasticity Least-squares finite elements |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X22000155 |
| work_keys_str_mv | AT lindaalzaben onthespectrumofthefiniteelementapproximationofathreefieldformulationforlinearelasticity AT fleuriannebertrand onthespectrumofthefiniteelementapproximationofathreefieldformulationforlinearelasticity AT danieleboffi onthespectrumofthefiniteelementapproximationofathreefieldformulationforlinearelasticity |