Jaekwang,
I am little bit confused by weak form for advection problem written in step-9
tutorial
in the its tutorial, in the middle of the line, it says that...
I am little bit unsure the red-marked form,
I think you forgot the formula.
From the whole boundary integral, we put inflow case, to the right hand side,
and remaining part on left-hand-side is cases other than inflow condition
so I thought, this should be..
<https://lh3.googleusercontent.com/-_-hS916j4W8/WZICJB_jYWI/AAAAAAAABEU/scEwE0R6BlYkOd4_vFYaAm-8rLuEOdqoACLcBGAs/s1600/Screen%2BShot%2B2017-08-14%2Bat%2B2.59.36%2BPM.png>
the left hand side term is boundary that is not inflow case...
I'm not entirely sure I understand your question, but you arrive at the weak
formulation by
* taking the original PDE, multiplying it with the modified test functions,
and integrating by parts
* on both sides of the equations, add the term
(beta.n v_h, u_h)_{inflow boundary}
* on the right hand side, replace u_h by g_h on the inflow boundary part
The key step that may not have been obvious is that in the second step, we add
the same thing to both sides of the equation. The equation therefore must
remain the same.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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