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MINI Element for the Navier–Stokes System in 3D: Vectorized Codes and Superconvergence
Volume 35, Issue 2 (2024), pp. 341–361
Pub. online: 23 February 2024      Type: Research Article      Open accessOpen Access
Received
1 May 2023
Accepted
1 February 2024
Published
23 February 2024

Abstract

A fast vectorized codes for assembly mixed finite element matrices for the generalized Navier–Stokes system in three space dimensions in the MATLAB language are proposed by the MINI element. Vectorization means that the loop over tetrahedra is avoided. Numerical experiments illustrate computational efficiency of the codes. An experimental superconvergence rate for the pressure component is established.

References

 
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Biographies

Kučera Radek
https://orcid.org/0000-0002-8237-5177
radek.kucera@vsb.cz

R. Kučera is a full professor at Department of Mathematics and Descriptive Geometry at the VSB–Technical University of Ostrava, Czech Republic. His research interests include numerical linear algebra and numerical optimization with applications to contact problems for linear elastic bodies and flow problems with stick-slip boundary conditions.

Arzt Vladimír
vladimir.arzt@vsb.cz

V. Arzt is a PhD student at Department of Applied Mathematics at the VSB–Technical University of Ostrava, Czech Republic. His research interests include numerical optimization with applications to solving PDEs with the stick-slip boundary conditions and shape optimization problems.

Koko Jonas
jonas.koko@uca.fr

J. Koko is an associate professor of applied mathematics in School of Computer Science at Université Clermont Auvergne, France. His research interests include scientific/parallel computing, numerical optimization and applications to nonlinear mechanics.


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Keywords
Navier–Stokes system mixed finite element method MINI element convergence rate MATLAB

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