I integrating by parts on the phi * grad a. First time gets it into weak
form. Then a second time gets it back into the original equation and into
strong form as I understand it. Is this misunderstood?
On Friday, July 19, 2024 at 2:01:32 PM UTC-6 Wolfgang Bangerth wrote:
> On 7/19/24 13:35, Sean Johnson wrote:
> >
> > The term shown in the graph is from a fairly simple equation. It arises
> from
> > the need of using the Local Discontinuous Galerkin method for a second
> order
> > derivative in one of the hyperbolic equations. The equation being solved
> is:
> > grad a - q = 0
> > where a is the variable that is equal to 1 everywhere and q is to be
> solved
> > for. I try and do a strong form and end up with:
> >
> > \int_cell phi * q = \int_cell phi * grad a + \int_face phi*( {{a}} -
> > a_interior ) * normal
> >
> > where {{a}} is the average of the values of a on the faces.
> >
> > This though leads to the horribly broken solution of q that has positive
> and
> > negative values and jumps when it should be smooth. Is the answer to use
> a
> > limiter or filter at this point? I am new to discontinuous galerkin but
> I
> > haven't seen a filter or limiter being used in local discontinuous
> galerkin
> > before.
>
> I'm not an expert on DG either, so don't know how to help. But let me ask
> you
> where the the face integral comes from? You're not integrating by parts
> anywhere, after all.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
>
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