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
