On 01/23/2014 10:02 AM, Jan Blechta wrote: > On Thu, 23 Jan 2014 09:54:34 -0800 > Nikolaus Rath <[email protected]> wrote: > >> On 01/23/2014 09:25 AM, Jan Blechta wrote: >>> On Thu, 23 Jan 2014 18:19:45 +0100 >>> Jan Blechta <[email protected]> wrote: >>> >>>> On Thu, 23 Jan 2014 08:53:13 -0800 >>>> Nikolaus Rath <[email protected]> wrote: >>>> >>>>> On 01/23/2014 04:19 AM, Jan Blechta wrote: >>>>>> On Wed, 22 Jan 2014 11:39:30 -0800 >>>>>> Nikolaus Rath <[email protected]> wrote: >>>>>> >>>>>>> Hi Jan, >>>>>>> >>>>>>> It was my impression from the other thread that I could handle >>>>>>> the problem of multiple solutions by giving the nullspace to the >>>>>>> solver. But I'll try the Laplace constraint as well. >>>>>>> >>>>>>> But then, even with u constrained, I still need to somehow put >>>>>>> the same constraint on the test functions, don't I? That's the >>>>>>> part I'm struggling with. >>>>>> >>>>>> Sure. This is why it seems logical to me to constraint both trial >>>>>> and test space by Laplace equation. Nevertheless I did not think >>>>>> it over a much. >>>>> >>>>> >>>>> For what it's worth, it seems logical to me as well... I just >>>>> don't know how to impose the second constraint. >>>> >>>> Check >>>> http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/neumann-poisson/python/documentation.html >>>> >>>> Testing by (v, 0) and (v + c, 0) gives linearly dependent >>>> equations - in fact, the same. Similar construction can apply to >>>> your problem. >>> >>> Here, I meant (v, 0) and (v + arbitrary_constant, 0). And it holds >>> because "the sufficient condition" >>> \int f \dx + \int g \ds = c |\Omega| >>> is fulfilled. >> >> >> I'm afraid I'm completely lost. What do you mean with "Testing by (v, >> 0) and (v + arbitrary_constant, 0)", and what is |\Omega|? The >> sufficient condition on the above link doesn't have this term... > > "Testing by foo" means set test function in the equation to foo and > observe... > > |\Omega| is a measure of \Omega. > > You get "the sufficient condition" > \int f \dx + \int g \ds = c |\Omega| > when testing by (v, d) := (1, 0). It is in quotes, as it is no longer a > sufficient condition but rather a property of the solution. Actually, > the value of the multiplier c.
Thanks, that makes sense to me now. But how does that relate to imposing constraints on the test function? Best, Nikolaus _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
