Consider the standard CahnHilliard free energy, augmented by a nonlocal interaction term which measures the $H^{1}$ norm of a zeromean function. Could someone point me to a reference where this nonlocal term is numerically approximated for a function on a compact domain, but without assuming periodicity? The periodic case is handled, for example, in a paper by Choksi et al in SIAM J. Appl.Math., 2009. Specifically, any strategies which avoid a Poisson solve would be welcome.
