Colin, 1) What do you mean by not supporting elimination within hybridized methods? 2a) So if I use the interior penalty method that would be using DG1 space. Would projecting between DG1 and DG0 spaces result in a loss of accuracy and information? 2b) For the advection demo, I modified it so that it solves a transient problem, but when I use DG1 elements I seem to get answers that violate the maximum principles. Does the formulation in the demo only work for DG0 elements or could it also potentially work for DG1 elements? I currently do not have access to any journals (since its 2:30 am where I am right now), so I am not sure if the answer to this particular question lies in the papers/books you guys have listed or not. Thanks, Justin On Tuesday, September 29, 2015, Colin Cotter <colin.cotter@imperial.ac.uk <javascript:_e(%7B%7D,'cvml','colin.cotter@imperial.ac.uk');>> wrote:
Dear Justin, Since we don't support elimination within hybridized methods for DG at present, your best option is to use the interior penalty method since it can be applied in primal form. See for example: Arnold, D. N., Brezzi, F., Cockburn, B., & Marini, L. D. (2002). Unified analysis of discontinuous Galerkin methods for elliptic problems. *SIAM journal on numerical analysis*, *39*(5), 1749-1779.
all the best -cjc
On 29 September 2015 at 08:48, Justin Chang <jychang48@gmail.com> wrote:
Hi all,
I am doing an operator-splitting time-stepping scheme for an advection-diffusion-reaction system. That said, I have two maybe related questions.
1) I see that you guys have a nice low order DG scheme for the advection equation, and was wondering if a similar discretization can be made for the transient diffusion equation.
I have seen plenty of nodally discontinuous galerkin methods like SIPG, but is it possible to discretize that equation using DG0 elements (i.e., piece-wise constant)? In other words, I am wondering if it’s possible to come up with a finite-volume-like weak form of the following:
du/dt - div(D*grad(u)) = f
where D is the diffusivity tensor (dim by dim) and we use backward euler time-stepping.
2) Suppose I use the DG0 formulation for advection and CG1 for diffusion, in operator splitting, the “initial condition” for one operator is the computed solution from the previous operator. That is, if I first solve the advection equation for one time step, that solution becomes the initial condition for the diffusion equation. If I have to pass back and forth between DG0 and CG1 solution spaces, will I lose a lot of accuracy due to projecting or “smoothening” out the data?
Thanks, Justin _______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake
-- http://www.imperial.ac.uk/people/colin.cotter
www.cambridge.org/9781107663916