Efficient MATLAB Codes for the 2D/3D Stokes Equation with the Mini-Element

Article type: Research Article

Authors: Koko, Jonas^{; *}

Affiliations: LIMOS, Université Blaise Pascal – CNRS UMR 6158, ISIMA, Campus des Cézeaux – BP 10125, 63173 Aubière cedex, France. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We propose a fast MATLAB implementation of the mini-element (i.e. P1-Bubble/P1) for the finite element approximation of the generalized Stokes equation in 2D and 3D. We use cell arrays to derive vectorized assembling functions. We also propose a Uzawa conjugate gradient method as an iterative solver for the global Stokes system. Numerical experiments show that our implementation has an (almost) optimal time-scaling. For 3D problems, the proposed Uzawa conjugate gradient algorithm outperforms MATLAB built-in linear solvers.

Keywords: finite element method, Stokes problem, Uzawa conjugate gradient, MATLAB

Journal: Informatica, vol. 30, no. 2, pp. 243-268, 2019