Thanks. I have not had time to sort it out, any more than trying to figure out how to get hotmail to now mark reply text, but I saw some indication that part of the problem may simply be Fick's Law dropping some physics. Any numerical think that looks hokey may simply be addding back some physics but it may be nice to know that that is the case.
And certainly 1-D FD is not the end of the story but I'm finding it helpful to understand some things. Not everything need be general- conformal mapping has its uses for example- and sometimes "tricks' or interesting observations turn out to point to better understanding. ________________________________________ From: Alexander Lindsay <[email protected]> Sent: Wednesday, January 18, 2017 3:05 PM Cc: [email protected] Subject: Re: [Libmesh-users] dealing with spurious oscillations in xvection diffusion equations I'll throw out that there's some interesting work being done on advection problems over in the MOOSE framework. You can see this issue in particular which demonstrates use of Discontinuous Galerkin -> Finite Volume to eliminate oscillations (with some really awesome graphics thrown in): https://github.com/idaholab/moose/issues/7967 On 01/17/2017 03:48 PM, Roy Stogner wrote: > On Sun, 15 Jan 2017, Mike Marchywka wrote: > >> http://am2012.math.cas.cz/proceedings/contributions/madden.pdf > This is actually kind of dumbfounding: Fix Your Solutions With One > Weird Trick That Numerical Analysists Hate! I wonder if there's any > extension to 2D/3D? Any way to express the algorithm as a single weak > formulation that gives you a solution function rather than a weird two > phase solve that gives a set of solution points? > > IIRC a lot of FEM stabilization methods history could be (over) > simplified as "(1) see what works for finite differences on uniform > grids, (2) figure out how to copy it in a finite element setting, (3) > figure out how to make it more sensible under some theoretical > criteria, which often makes it better or more generalizable in > practice too". But most of the important step (1) work happened > before I was born, yet this paper (well, the 2007 paper they cite) > sounds like a real fresh entry in that vein. > >> Interested if anyone cares to comment on current status and libmesh >> facilities >> that may be relevant or if this is just a "lmgtfy" case. I gathered the >> normal >> approaches were largely things that modify the apparent diffusivity >> which does not seem to be a lot different from anything else you may add to >> a system. > Most numerical stabilization schemes do boil down into "adding > diffusivity" one way or another, but it's not as hokey as it sounds. > The trick is to do what's called "consistent stabilization": in the > finite element sense, consistent stabilization changes the weak > formulation in such a way that the exact solution to the problem is > still a solution to the stabilized weak problem. This (as well as > making sure the effects are anisotropic in 2D/3D) is generally enough > to get you a good solution (even an exact interpolant, in 1D!) without > smearing out real features. > --- > Roy > > ------------------------------------------------------------------------------ > Check out the vibrant tech community on one of the world's most > engaging tech sites, SlashDot.org! http://sdm.link/slashdot > _______________________________________________ > Libmesh-users mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/libmesh-users ------------------------------------------------------------------------------ Check out the vibrant tech community on one of the world's most engaging tech sites, SlashDot.org! http://sdm.link/slashdot _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users ------------------------------------------------------------------------------ Check out the vibrant tech community on one of the world's most engaging tech sites, SlashDot.org! http://sdm.link/slashdot _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
