Discontinuous Galerkin Stokes Problem

Aubium · April 3, 2024, 11:38pm

Good evening members,

I’m struggling with the implementation of an incompressible Stokes equation using Disontinuous Galerkin method. Here are my questions :

How to write the integral on border edges ?
How to write the projection into Pk of u_h ? (pi_k(u_h)) ?

And if you have a sample, it would be of great help. Thank you !

frederichecht · April 4, 2024, 4:34am

First read example on DG for Laplace equation

github.com

FreeFem/FreeFem-sources/blob/master/examples/tutorial/LapDG2.edp

//    Discontinous Galerlin Method
//   based on paper from 
// Riviere, Beatrice; Wheeler, Mary F.; Girault, Vivette
// title: 
// A priori error estimates for finite element 
// methods based on discontinuous approximation spaces
//  for elliptic problems.
//  SIAM J. Numer. Anal. 39 (2001), no. 3, 902--931 (electronic).
//  ---------------------------------
//  Formulation given by Vivette Girault
//  ------ 
// Author: F. Hecht , december 2003
// -------------------------------
//   nonsymetric bilinear form
//   ------------------------
//  solve $ -\Delta u = f$ on $\Omega$ and $u= g$ on $\Gamma$
//  on intalledges :
// the edge are see nTonEdge times so we / nTonEdge
// remark: nTonEdge =1 on border edge and =2 on internal 
// we are in a triangle normal is the exterior normal

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Aubium · April 4, 2024, 4:52am

(post deleted by author)

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Discontinuous Galerkin Stokes Problem

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