On Mon, 6 Oct 2014, John Peterson wrote: > Ah, I can almost hear Professor Demkowicz saying "all norms on > finite dimensional vector spaces are equivalent" :-)
Hah, I should have known someone would bring that up! :-) They generate equivalent topologies, but they're not equal metrics, and it's not an unimportant difference for defining a ball as "converged". Worse, the differences between them diverge with the growth of the "mass matrix" condition number, i.e. as you refine the mesh. I'm actually unsure what this means in practice, though. On the one hand, your maximum solver tolerance depends on what level of error you're willing to tolerate, and that error is usually best represented in something equivalent to the H1 norm. On the other hand, quadratic Newton convergence gives you a lot of leeway, and your minimum solver tolerance usually depends on where you expect assembly floating point error to start screwing you up, for which my dumb guess would be that an algebraic vector norm or a functional norm based on your Jacobian might be most appropriate. --- Roy ------------------------------------------------------------------------------ Slashdot TV. Videos for Nerds. Stuff that Matters. http://pubads.g.doubleclick.net/gampad/clk?id=160591471&iu=/4140/ostg.clktrk _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
