MINI Element for the Navier–Stokes System in 3D: Vectorized Codes and Superconvergence

Kučera, Radek; Arzt, Vladimír; Koko, Jonas

doi:10.15388/24-INFOR543

Informatica

MINI Element for the Navier–Stokes System in 3D: Vectorized Codes and Superconvergence

Volume 35, Issue 2 (2024), pp. 341–361

Radek Kučera

Vladimír Arzt Jonas Koko

https://doi.org/10.15388/24-INFOR543

Pub. online: 23 February 2024 Type: Research Article

Open 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.

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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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