How can we define the initial value for Cahn-Hilliard problem (links) using FEM in MMA?
Complete test code (I am using MIXED formulation for C1 Problem):
Needs["NDSolve`FEM`"]
\[CapitalOmega]=ImplicitRegion[{0<=x<=1,0<=y<=1},{x,y}];
RegionPlot[\[CapitalOmega],PlotRange->{{0,1},{0,1}}]
Mobi = 1.0; lame = 0.01;
op1 = \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(u[t, x, y]\)\) - Mobi.\!\(
\*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(v[t, x, y]\)\)
op2 = v[t, x, y] -
200 u[t, x, y] (1 - 3 u[t, x, y] + 2 u[t, x, y]^2) + lame.\!\(
\*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[t, x,
y]\)\(\ \)\)
Subscript[\[CapitalGamma], N1] =
NeumannValue[Mobi* lame.u[t, x, y], {0 <= x <= 1, 0 <= y <= 1}]
{nufun, nvfun} =
NDSolveValue[{op1 == Subscript[\[CapitalGamma], N1], op2 == 0}, {u,
v}, {t, 0, 100}, {x, y} \[Element] \[CapitalOmega]];
Dot
s afterMobi
andlame
have to be removed and you have not specified boundary conditions forv
. $\endgroup$NDSolve
. $\endgroup$