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## Re: [Libmesh-users] AMR in 3D

 Re: [Libmesh-users] AMR in 3D From: John Peterson - 2007-04-04 14:23:25 ```Roy Stogner writes: > On Wed, 4 Apr 2007, Luca Antiga wrote: > > > I could live with non zero values on the zero velocity faces, but aren't > > those a bit large (10% of the top face velocity)? > > Yes, but then Gibbs' type ringing usually is large. What's worse: as > you refine the mesh the boundary condition approximation will converge > in the L2 norm, but it can't converge in L_infinity.. > > > I'm just worried that the situation might go out of control in > > complicated geometries, so that's why I'm a bit picky on this > > problem. > > It's not the geometry that's controlling the problem, it's the > discontinuity in the boundary conditions. > I think John's had somewhat smoother results by using an H1 instead > of L2 boundary penalty, but when you try to force a continuous > approximation function to take on discontinuous values, there's > really no good way for it to react. Actually, I couldn't get the H1 projection to work (in 2D). I tried penalizing the tangential derivatives, to e.g. enforce du/dx=dv/dx=0 along the lid. One thing that seemed to help a bit (at least in 2D) was to use the "lumped" L2 projection (e.g. ex13). If memory serves, that solution "looked" slightly better (at least in 2D). > Many people give up and just regularize the problem boundary > conditions. Indeed, the hyperbolic tangent-type regularized boundary conditions seem to be fairly standard in the literature for this type of problem. If we just want to be sure Stokes+AMR+Tets is working, let's try a test problem with continuous data? -J ```