# FEM giving “ … is not a polynomial error”

Executing the program below I get the

... is not a polynomial

error message. I don't have an idea why I am getting this -- any suggestions?

ClearAll["Global*"]

Needs["NDSolveFEM"]

Q = 60;

A = 4000;

nb = 0.42;

dens = 1.48;

Co = 0.05;

Vx = Q/A;

Dx = 73.51*Vx + 0.282;

R = 1 + (dens/nb)*(0.9292/(1 + 0.092*Ccu[x, t])^2);

reator = Dx*D[Ccu[x, t], x, x] - Vx*D[Ccu[x, t], x] -
R*D[Ccu[x, t], t];

initial = Ccu[x, 0] == 0;

b1 = {Ccu[0, t] == Co, Ccu[300000, t] == 0};

regiao = ImplicitRegion[True, {{x, 0, 500000}}];

solucao =
NDSolve[{reator == 0, initial,
DirichletCondition[Ccu[x, t] == Co, x == 0],
DirichletCondition[Ccu[x, t] == 0, x == 100000]},
Ccu, {t, 0, 100000}, {x} ∈ regiao]


CoefficientArrays::poly: -(1+3.27432/(1+0.092 Ccu)^2) Ccu\$11498-(3 Ccu\$11499)/200 + 1.38465 Ccu\$11500 is not a polynomial. >> NDSolve::femper: PDE parsing error of {-(1+3.27432/(1+0.092 Ccu)^2) Ccu\$11498-(3 Ccu\$11499)/200+1.38465 Ccu\$11500}. Inconsistent equation dimensions. >>

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CoefficientArrays::poly: -(1 + 3.27432/(1 + 0.092 Ccu)^2) Ccu11498 - (3 Ccu11499)/200 + 1.38465 Ccu$11500 is not a polynomial. >> First note that Ccu is your dependent variable in your PDE. The expression being complained about has several variables, Ccu and ones like Ccu$11498.. (The ones like Ccu\$11498 are internal, localized variables representing the derivatives of Ccu in the PDE). Since Ccu appears in the denominator, the expression is not a polynomial. You can call CoefficientArrays on the expression to see the identical message.
As I pointed out in Kernel quits without error in NDSolveValue, this error should be caught internally and the more useful error NDSolve::femnonlinear` returned in its place.