In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7-32] to the Virtual Element Method for linear elasticity problems based on the Hellinger-Reissner principle. To illustrate such a technique, we focus on a specific 2D scheme, but other methods and 3D problems can be considered as well. We also show how to design a better approximation of the displacement field using a straightforward post-processing procedure. The numerical experiments confirm the theory for both two and three-dimensional problems.
Dassi, F., Lovadina, C., Visinoni, M. (2021). Hybridization of the virtual element method for linear elasticity problems. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 31(14), 2979-3008 [10.1142/S0218202521500676].
Hybridization of the virtual element method for linear elasticity problems
Dassi F.;
2021
Abstract
In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7-32] to the Virtual Element Method for linear elasticity problems based on the Hellinger-Reissner principle. To illustrate such a technique, we focus on a specific 2D scheme, but other methods and 3D problems can be considered as well. We also show how to design a better approximation of the displacement field using a straightforward post-processing procedure. The numerical experiments confirm the theory for both two and three-dimensional problems.
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