On Tue, Oct 4, 2016 at 10:23 AM, Jed Brown <j...@jedbrown.org> wrote:
> Matthew Knepley <knep...@gmail.com> writes: > > > On Mon, Oct 3, 2016 at 9:51 PM, Praveen C <cprav...@gmail.com> 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? 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
