Hi all,
I would like ask today that possible factors that might affect, (badly)
accuracy of streamline diffusion method for pure hyperbolic equation.
I am solving hyperbolic equation , \nabla( beta \dot u ) = f(x), as it is
suggested in tutorial step-9,
Step-9 tutorial explained this very nicely, and I could get very
well-behaved solution when I use linear element for my test and basis
function.
But, I am not receiving well behaved solution when I use higher order for
my elements, the error in solution still has accuracy of O(h), not
O(h^2)...
I refered some references on Streamline Diffusion method, and papers tell
me that I can expect at least p+(1/2) accuracy..but my accuracy is always
O(h)... no matter the order of element I use.
So, I suspect that I am being caught by somewhere that is only first order
accurate.
My weak form formation is exactly same with tutorial 9
// Advection Term
scratch_data.fe_values.shape_value(i,q_point) * (
advection_directions[q_point] *
scratch_data.fe_values.shape_grad(j,q_point)) //(beta grad u)
// Stabilization term (Streamline Diffusion Method)
+ *tau * * ( advection_directions[q_point] *
scratch_data.fe_values.shape_grad(i,q_point) )
*(advection_directions[q_point] *
scratch_data.fe_values.shape_grad(j,q_point))
For tau , which determines the strength of diffusion term, was chosen to be
'0.1h'. (Should this be chosen more wisely? Otherwise, I cannot expect
'p+(1/2)' order for error?
Another possible source of error might come from Integration Gauss
quadrature,
but the weak form (v,beta \cdot \nabla u) is locally '2p-1' polynomial, and
I have used enough Gauss Quadrature order for integrating the weak form..
Any one has idea on possible point I will have to check to attain (p+1/2)
error behavior ?
Always thank you,
Regards,
Jaekwang Kim
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