For a weak solution, you can split the boundary integral (coming from integration by parts) into a normal and a tangential part. With no-normal flux contraints you remove the normal part only, so the tangential part needs to be written as a boundary integral on the RHS of your PDE unless it is zero in your manufactured solution. You can find more info in Ern/Guermond in the "variations on boundary conditions" for Stokes.
On Mon, Apr 15, 2019 at 10:01 AM <[email protected]> wrote: > > Hi Wolfgang > > Thanks for your reply. > > That was actually what I had done previously. I've tried all sorts by looking > at the values on different boundaries, indicators, tried multiple problems, > etc before I had asked the question, which is why I came to thinking it had > something with the implementation. > > Thanks for your suggestions - I had another thought, that perhaps it might be > a mathematical issue. On a no normal flux condition in the Stokes case, am I > correct in assuming that for the reamining components (1- nxn)(n.[pI-2e(u)]) > for the boundary ocndition, if homogenous (=0) then it disappears within the > weak form, and if non zero, it needs to be imposed weakly? > > or does something else need to take place for this? > > On Monday, April 15, 2019 at 3:33:36 PM UTC+1, Wolfgang Bangerth wrote: >> >> >> > The mesh has over 100000 cells in it, it is super refined. And oddly, >> > when >> > the refinement level is less, it doesn't blow up. It's only after a >> > certain point. >> > it is an even global refinement, starting from a hyper divided >> > rectangle. >> > no fancy refinement. >> > >> > I only realised this as I wasn't getting the right convergence rates >> > for v >> > at the lower refinement levels so I just kept going up to see if it >> > eventually did and it blew up. >> > Until this point, at the refinement levels that work, the pressure >> > converges correctly at two consecutive degrees, and so does v at the >> > higher degree. but at the lower degree, the convergence rates for v >> > were >> > decreasing with refinement. >> > That;s why I continued to refine then came across this situation. >> > >> > Seeing that it is only at the bottom, and noticing that if I used >> > Dirichlet condition on that boundary, then the solution doesn't blow up >> > and converges correctly, I can only assume it's to do with the normal >> > flux >> > condition there, which i think I'm imposing correctly. >> >> Jane -- I don't think anyone other than you is in a position to figure this >> out. I've learned to debug problems with a mind set of assuming that >> everything I believe is correct may in fact not. So when you say >> "I can only assume it's to do with the normal flux condition there, which >> i think I'm imposing correctly" >> then my approach is to assume that they are not imposed correctly, and to >> write code that helps me to *verify* that it is. >> >> As an example, even though you think that you've set the boundary indicators >> correctly at all cells on the bottom, this may not be the case for whatever >> reason. Write a loop over all cells and all boundary faces and *output* >> location and boundary indicator, to make sure it is. Go through this sort of >> procedure for everything you *believe* should be true to make sure that it >> *is* true. >> >> I'm sorry I have no other suggestions for what to do. We've all been in your >> situation where stuff doesn't work for reasons that seem completely >> mysterious. The successful among us are the ones who have built the mental >> and >> computer skills to figure out what the cause is. Among the mental skills is >> the ability to assume that what one believes to be true (because one has >> written the code) may not be so. The computer skills is then to use a >> debugger >> or print statements in the right places to verify that something is indeed >> the >> case or not, and to narrow down the possible root causes. >> >> Best >> W. >> >> >> -- >> ------------------------------------------------------------------------ >> Wolfgang Bangerth email: [email protected] >> www: >> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.math.colostate.edu_-7Ebangerth_&d=DwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=QVz-0qa-BE17tx8qPdxGM1rRo9ff7D68_fU_ptB7amo&s=54A9voRgVztKomopsSD34VYdFjTc_5ZY7Lj3-cyi2SE&e= >> > -- > The deal.II project is located at > https://urldefense.proofpoint.com/v2/url?u=http-3A__www.dealii.org_&d=DwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=QVz-0qa-BE17tx8qPdxGM1rRo9ff7D68_fU_ptB7amo&s=2YX98RoE1A9bLcn1QbLuBECzNPFA4vb6_oBwLDbzKR0&e= > For mailing list/forum options, see > https://urldefense.proofpoint.com/v2/url?u=https-3A__groups.google.com_d_forum_dealii-3Fhl-3Den&d=DwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=QVz-0qa-BE17tx8qPdxGM1rRo9ff7D68_fU_ptB7amo&s=RkLbASOUUx7tA80Bri9yrzo98EtTJd37rlweHmB4oPg&e= > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > For more options, visit > https://urldefense.proofpoint.com/v2/url?u=https-3A__groups.google.com_d_optout&d=DwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=QVz-0qa-BE17tx8qPdxGM1rRo9ff7D68_fU_ptB7amo&s=xZmdJOK1R0lGAXwZYXtmfo7Cs6OKj9hyECKrMRnxZgU&e=. -- Timo Heister https://urldefense.proofpoint.com/v2/url?u=http-3A__www.sci.utah.edu_-7Eheister_&d=DwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=QVz-0qa-BE17tx8qPdxGM1rRo9ff7D68_fU_ptB7amo&s=p4B6GuaoOEGN-eVO-4uigc0gYaBJZBeSRC0wj9KNQ20&e= -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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