An Enriched Galerkin Method for the Stokes Equations

10/11/2021
by   Son-Young Yi, et al.
0

We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise linear space for velocity by adding an additional degree of freedom which corresponds to one discontinuous linear basis function per element. Thus, the total number of degrees of freedom is significantly reduced in comparison with standard conforming, non-conforming, and discontinuous Galerkin schemes for the Stokes equation. We show the well-posedness of the new EG approach and prove that the scheme converges optimally. For the solution of the resulting large-scale indefinite linear systems we propose robust block preconditioners, yielding scalable results independent of the discretization and physical parameters. Numerical results confirm the convergence rates of the discretization and also the robustness of the linear solvers for a variety of test problems.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 19

page 20

page 21

09/22/2021

A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence

A discontinuous Galerkin pressure correction numerical method for solvin...
03/22/2021

A matrix-theoretic spectral analysis of incompressible Navier-Stokes staggered DG approximation and related solvers

The incompressible Navier-Stokes equations are solved in a channel, usin...
11/22/2018

An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations

We present and analyze a new embedded--hybridized discontinuous Galerkin...
05/19/2021

Preconditioning for a pressure-robust HDG discretization of the Stokes equations

We introduce a new preconditioner for a recently developed pressure-robu...
04/28/2021

Uniform block diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes problem and linear elasticity

We propose a uniform block diagonal preconditioner for the condensed H(d...
02/14/2020

HDG and CG methods for the Indefinite Time-Harmonic Maxwell's Equations under minimal regularity

We propose to use a hybridizable discontinuous Galerkin (HDG) method com...
04/20/2020

Alias-free, matrix-free, and quadrature-free discontinuous Galerkin algorithms for (plasma) kinetic equations

Understanding fundamental kinetic processes is important for many proble...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.