On Tue, Oct 4, 2016 at 10:43 AM, Jed Brown <[email protected]> wrote:
> Matthew Knepley <[email protected]> writes: > > > On Tue, Oct 4, 2016 at 10:23 AM, Jed Brown <[email protected]> wrote: > > > >> Matthew Knepley <[email protected]> writes: > >> > >> > On Mon, Oct 3, 2016 at 9:51 PM, Praveen C <[email protected]> wrote: > >> > > >> >> DG for elliptic operators still makes lot of sense if you have > >> >> > >> >> problems with discontinuous coefficients > >> >> > >> > > >> > This is thrown around a lot, but without justification. Why is it > better > >> > for discontinuous coefficients? The > >> > solution is smoother than the coefficient (elliptic regularity). Are > DG > >> > bases more efficient than high order > >> > cG for this problem? I have never seen anything convincing. > >> > >> CG is non-monotone and the artifacts are often pretty serious for > >> high-contrast coefficients, especially when you're interested in > >> gradients (flow in porous media). But because the coefficients are > >> under/barely-resolved, you won't see any benefit from high order DG, in > >> which case you're just using a complicated/expensive method versus > >> H(div) finite elements (perhaps cast as finite volume or mimetic FD). > >> > > > > I was including H(div) elements in my cG world. Is this terminology > wrong? > > It's not a continuous basis.... > > Perhaps ambiguous. > I think cG should refer to Conforming Galerkin, since that is really what is implied. DG and H(div) are both non-conforming. So I really want to cG/nG dichotomy. Matt -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
