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Efficient MATLAB Codes for the 2D/3D Stokes Equation with the Mini-Element
Volume 30, Issue 2 (2019), pp. 243–268
Pub. online: 1 January 2019      Type: Research Article      Open accessOpen Access
Received
1 February 2018
Accepted
1 December 2018
Published
1 January 2019

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.

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Biographies

Koko Jonas
jonas.koko@uca.fr

J. Koko is an associate professor in applied mathematics at the Computer Science School at the University Clermont-Auvergne. His research interests include numerical optimization with applications to Partial Differential Equations (PDE) and parallel computing, vectorized MATLAB codes for the numerical approximation of PDEs.


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© 2019 Vilnius University
Open access article under the CC BY license.

Keywords
finite element method Stokes problem Uzawa conjugate gradient MATLAB

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