Dear Daniel, Thanks for your reply! Essentially what I was trying to do is patch together two product spaces: ([H1_0]^2, L^2_0) in one part of the domain and ([H1_0]^2, L^2_0) in another, with an interface condition to ensure solvability for my problem (Stokes in one part of the domain, laplace in another). The interface condition was chosen such that there would be no jump of the velocity gradient across the interface (this was done by choosing an L2_0 pressure that goes in the right-hand side). Unfortunately this did not work in the implementation phase and I ended up getting a jump of the velocity gradient across the interface. At the moment I don't know if this is a coding bug, or an erroneous choice of spaces. To be honest I expected weak differentiability to be enough to ensure a zero velocity gradient jump across the interface too. As such, I was thinking how I should choose my spaces to ensure gradient continuity across the interface to see if this would fix my problem but I do not know how to enforce that in deal.ii. As such, any advice on how to do that would be great.
Kind regards, Geogios On Monday, August 20, 2018 at 2:31:39 PM UTC+1, Daniel Arndt wrote: > > Georgios, > > I am working on a combined stokes laplace problem (I also attach the >> code). Essentially I am solving stokes in one part of the domain and >> laplace in another. To this extend, I want my velocity to be both >> continuous and and have continuous first derivatives everywhere in my >> domain (including on between interfaces). My implementation is similar to >> step 46. I am choosing my spaces like I show below (in the stokes part and >> in the laplace part of my domain respectively): >> >> stokes_fe (FE_Q<dim>(stokes_degree+2), dim, >> >> FE_Q<dim>(stokes_degree+1), 1), >> >> laplace_fe (FE_Q<dim>(stokes_degree+2), dim, >> >> FE_Nothing<dim>(), 1), >> >> >> >> spaces with the intention of getting zero jump in the velocity gradient >> between the interfaces, however, this does not happen. I have taken care >> to choose my pressure in L^2_0 on both parts of the domain. Any suggestion >> on how I can enforce continuity of velocity gradients across the interface? >> > The (discrete) ansatz spaces you have chosen only imply continuity and > continuity of the gradients in tangential direction across faces. Hence, > you propably would need to modify your ansatz spaces to get continuity in > normal direction. > From a mathematical point of view, I would expect weak differentiability > to be sufficient though. > What is the (continuous) solution space for the continuous formulation of > your problem? > > In the end, the question is: Why do you need continuous gradients? > > Best, > Daniel > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
