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

Abstract

We propose a fast MATLAB implementation of the mini-element (i.e. $\mathit{P}1$ -Bubble/ $\mathit{P}1$ ) 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.