Hi Killian, It is not necessarily wrong to have a discontinuous forcing function since the projection of the RHS term is dealt with by the way you handle the LHS terms. If we were using a DG scheme on the LHS then one issue might be how the Reimann solver sees the forcing term. When you have a very energetic forcing term (i.e. your c*grad(v) ) you may have to take this into consideration in your Riemann solver as a source term if it is very large compared to the v *grad(u) term. If the RHS term is not significantly larger than the v* grad(u) term then I would have through just adding the term as you have suggested should be stable at least. Is there a reason you want it to be C0 continuous? You can project it onto a C0 space by inverting a mass matrix but this is obviously expensive. Alternatively you could average the value at the interface which is not so mathematically consistent but I think may work anyway. Cheers, Spencer. On 14 Dec 2016, at 13:43, Kilian Lackhove <lackhove@ekt.tu-darmstadt.de<mailto:lackhove@ekt.tu-darmstadt.de>> wrote: Dear List, i am trying to implement a source term based on the gradient of an auxiliary field in the APESolver. My problem is quite general, so i in terms of the simpler ADR solver, a minimal example would look like this: du / dt + v * grad(u) = c * grad(v) with u being a transported variable, v the advection velocity and c a constant. The problem is the gradient on the right hand side. I tried computing it by using ExpList::PhysDeriv(), but since the projection is not C1-continuous, this fails at the element edges. I attached an example plot to illustrate the problem. p0/rho0 uses the left axis, the gradient the right hand side one. Do you have any suggestions on how to handle the gradient term? Is there some other method i should use? Cheers, Kilian -- Kilian Lackhove, M.Sc. Fachgebiet für Energie- und Kraftwerkstechnik L1|08 114 Technische Universität Darmstadt Jovanka-Bontschits-Straße 2 D-64287 Darmstadt Germany Tel.: +49 6151 16 - 28915 Fax: +49 6151 16 - 6555 e-mail: lackhove@ekt.tu-darmstadt.de<mailto:lackhove@ekt.tu-darmstadt.de><grad_dg.pdf>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users Spencer Sherwin McLaren Racing/Royal Academy of Engineering Research Chair, Professor of Computational Fluid Mechanics, Department of Aeronautics, Imperial College London South Kensington Campus London SW7 2AZ s.sherwin@imperial.ac.uk<mailto:s.sherwin@imperial.ac.uk> +44 (0) 20 759 45052