SPUG on CG Elements

6 weeks ago by
I want to implement a SPUG Stabilization term in a 1D advection problem.
I'am reffering to this paper:

There a stabilization term is defined in equations 9-11.
As far as I understand the paper u,v would be functions in the normal continous garlerkin space, but the stabilization term is defined "cell-wise".

How do I define these stabilization terms cell-wise?

Best Regards,
Community: FEniCS Project

1 Answer

6 weeks ago by
There is nothing special that needs to be done.  The "dx" measure in FEniCS is already a sum of integrals over element interiors, so the stabilization terms can be integrated using it.  This is usually equivalent to integrating over the entire domain.  However, in the case of SUPG, there would be distributional contributions (Dirac deltas) when integrating the Laplacian of a function that has jumps in its first derivatives at element boundaries, so the stabilization terms are explicitly written as sums of integrals over element interiors, to emphasize that these contributions are not included.  The "cell-wise" quantity \(h_K\) used to define \(\tau_K\) can be obtained by
h = CellDiameter(mesh)​
cool, thank you for the explanation.
I will try to implement it and come back.
written 6 weeks ago by Moritz  
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