An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn Hilliard/Navier Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed.
We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering.
My life is not a Double Dare obstacle course and I am not the happy child beaming for the cameras under a cascade of slime.
We give local boundedness for very weak solutions of double obstacle problems.
This article mainly concerns double obstacle problems for second order divergence type elliptic equation divA x, u, ▽u) = divf(x).
end{aligned} (8 Owing to its governing influence on the finite interface width and its subsequent computational advantage, the double obstacle potential is used in all simulations of the present work.
In contrast to the double well potential, which is mostly used in the phase-field community, the double obstacle potential begin{aligned} w^{ob} phi )= {left{ begin{array}{ll} frac{16}{pi ^2}phi (1-phi ), &quad phi in mathcal {G} infty, &quadtext {else} end{array}right.
Beneficial for the double obstacle potential is the corresponding one-dimensional equilibrium phase-field profile, which is expressed as follows: begin{aligned} phi ^{ob}_{eq}(x) = {left{ begin{array}{ll} 0, &quad x < -0.125pi ^2epsilon, 0.5left(1+sin left({frac{4x}{pi epsilon }}right)right ), &quad x in [-0.125,0.125]pi ^2epsilon, 1, &quad x >0.125pi ^2epsilon end{array}right.
The algorithms are implemented, for both one and double obstacles, in Matlab and carried out on a Desktop computer of an Intel i5-3450S 2.80 GHz processor.
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