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).
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