I am trying to solve this PDE using the inactive form, however I ran into error stating that the: The PDE coefficient 0. does not evaluate to a numeric matrix of dimensions {2,1} at the coordinate {0.5,0.5}; it evaluated to 0. instead. This error appears after using the new diffusion expression, diff2s which is essential for my code. Here is the code
ClearAll["Global`*"]
(*Parameters*)
Dcoeff = 9.24*10^-11; Xmax = 0.015; tmax = 10^8; A =
Dcoeff*tmax/Xmax^2;
Na = 6.022*10^23; vw = 2.99*10^-29; B1 = 50; D1 = 0.1;
CSinitial = 1; CFinitial = 1/1000; DelU = -5; vfsb =
6.5*10^-26; a = 2.5;
(*Binding site profile*)
cs[xstar_] := CSinitial*(0.5 - 0.5*Tanh[B1*(xstar - D1)]);
(*Bound cargo*)
cb[xstar_, CF_] := (Na*cs[xstar]*CF*vw)/(Exp[DelU] + Na*CF*vw);
(*Steric potential*)
Uster[CF_, xstar_] := -(1 + a)^2*
Log[1 - cb[xstar, CF]*vfsb - CF*vfsb - cs[xstar]*vfsb];
(*Binding potential*)
Ubind := DelU;
(*Effective potential*)
Ueff[CF_, xstar_] := Uster[CF, xstar] + Ubind;
(*Diffusivity spatial function*)
phi[CF_, xstar_] := 1 - vfsb*(cb[xstar, CF] + CF + cs[xstar]);
Diff2s[CF_, xstar_] := (phi[CF, xstar]/(2 - phi[CF, xstar]))^2;
(*PDE in Inactive form*)
cEqn := (1 + (CSinitial/CFinitial)*
D[cb[xstar, cfree[tstar, xstar]], cfree[tstar, xstar]])*
D[cfree[tstar, xstar], tstar] ==
A*Inactive[Div][{0,
Diff2s[cfree[tstar, xstar],
xstar]*(cfree[tstar, xstar]*
Inactive[Grad][
Ueff[cfree[tstar, xstar], xstar], {tstar, xstar}][[2]] +
Inactive[Grad][
cfree[tstar, xstar], {tstar, xstar}][[2]])}, {tstar,
xstar}] + NeumannValue[0, xstar == 0];
(*Initial& boundary conditions*)
ic = cfree[0, xstar] == (0.5 - 0.5*Tanh[B1*(xstar - D1)]);
bc = DirichletCondition[cfree[tstar, xstar] == 0, xstar == 1];
(*Solve*)
sol = NDSolveValue[{cEqn, ic, bc},
cfree, {tstar, 0, 1}, {xstar, 0, 1},
Method -> {"PDEDiscretization" -> {"FiniteElement",
"MeshOptions" -> {"MaxCellMeasure" -> 0.00005}}}];
Grad[f[x, y, z], {x, y, z}], in 2D it's something likeGrad[f[x, y], {x, y}], now, what should it be in 1D? $\endgroup$