On 10 June 2014 10:44, Anders Logg <[email protected]> wrote: > On Tue, Jun 10, 2014 at 10:09:44AM +0200, Martin Sandve Alnæs wrote: > > To clarify, Kristian talks about the jump(f,n) version: > > > > jump(scalar,n) is vector-valued > > jump(vector,n) is scalar > > > > while I mixed up with the jump(f) version: > > > > jump(scalar) is scalar > > jump(vector) is vector-valued > > > > The jump(f) version gives the difference of the full value, while > > the jump(f,n) version gives the difference in normal component. > > I looked through the Unified DG paper that Kristian pointed to but > couldn't see any examples of vector-valued equations. >
Section 3.1, text below eqn. 3.2 definitions of avg and jump for functions 'q' and '\phi'. Kristian > > I also don't see the point in defining jump(v, n) for vector valued u > as in the paper. If the result of jump(v, n) is a scalar quantity, > there is no way to combine the normal n with the thing it should > naturally be paired with, namely the flux (or grad(u)). It only works > out in the special case of scalar elements. > > But perhaps adding tensor_jump() is the best solution since that paper > is the standard reference for DG methods. > > (I'll ask Douglas Arnold about this, if he has not seen this > already. Maybe I am missing something obvious.) > > > However, if I didn't mess up some signs I think you can write your term > like > > > > 0.5*dot(jump(Dn(u)), jump(v)) > > > > which seems much more intuitive to me (although I'm not that into DG > scheme > > terminology). > > Yes, that looks correct but I don't think it is intuitive since it > does not involve the avg() operator which is naturally paired with the > jump() operator in most DG formulations. > > -- > Anders > > > > On 10 June 2014 09:05, Kristian Ølgaard <[email protected]> wrote: > > > > > > On 9 June 2014 20:58, Martin Sandve Alnæs <[email protected]> > wrote: > > > > > > I object to changing definitions based on that it would work out > nicely > > for one particular equation. The current definition yields a > scalar > > jump for both scalar and vector valued quantities, and the > definition > > was chosen for a reason. I'm pretty sure it's in use. Adding a > > tensor_jump on the other hand wouldn't break any older programs. > > > > Maybe Kristian has an opinion here, cc to get his attention. > > > > > > I follow the list, but thanks anyway. > > > > The current implementation of the jump() operator follows the > definition > > often used in papers (e.g. UNIFIED ANALYSIS OF DISCONTINUOUS GALERKIN > > METHODS > > FOR ELLIPTIC PROBLEMS, arnold et al. > http://epubs.siam.org/doi/abs/10.1137/ > > S0036142901384162) > > > > where the jump of scalar valued function result in a vector, and the > jump > > of a vector valued function result in a scalar. > > > > Adding the tensor_jump() function seems like a good solution in this > case > > as I don't see a simple way of overloading the current jump() > function to > > return the tensor jump. > > > > Kristian > > > > > > > > Martin > > > > 9. juni 2014 20:16 skrev "Anders Logg" <[email protected]> > følgende: > > > > > > On Mon, Jun 09, 2014 at 11:30:09AM +0200, Jan Blechta wrote: > > > On Mon, 9 Jun 2014 11:10:12 +0200 > > > Anders Logg <[email protected]> wrote: > > > > > > > For vector elements, the jump() operator in UFL is > defined as > > follows: > > > > > > > > dot(v('+'), n('+')) + dot(v('-'), n('-')) > > > > > > > > I'd like to argue that it should instead be implemented > like > > so: > > > > > > > > outer(v('+'), n('+')) + outer(v('-'), n('-')) > > > > > > This inconsistency has been already encountered by users > > > http://fenicsproject.org/qa/359/ > > discontinuous-galerkin-jump-operators > > > > Interesting! I hadn't noticed. > > > > Are there any objections to changing this definition in UFL? > > > > > > > > > > >
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