I'm trying to use NDSolve to solve Laplace's Equation over a particular region of 2D space. When I try to get an answer I receive an obscure error message that does not appear to be documented anywhere on the Wolfram site.

NDSolve::femcbtd: A coordinate that is part of the region NDSolveFEMNumericalRegion[ImplicitRegion[<<1>>,{z,r}],{{-(102939420054182/5146971002709099),(1<<13>>2)/(5<<14>>9)},{0,<<1>>}}] could not be found in time 1.`. Either specify a coordinate that is part of the region via the "TestData" option or increase the time to find such a coordinate via the option TimeConstraint. >>

I cannot get NDSolve to accept either of the options "TestData" or TimeConstaint

Here's the code:-

R1 = 0.006;
R2 = 0.015;
Rm = 0.015 Sqrt[2];
Ur = 3500.;
z0 := Sqrt[r^2/2 - R^2/2 + Rm^2 Log[R/r]]
z1[r_] = z0 /. R -> R1;
z2[r_] = z0 /. R -> R2;
Off[InverseFunction::ifun];
r1 = InverseFunction[z1];
r2 = InverseFunction[z2];

\[CapitalOmega] = 
  ImplicitRegion[{r >= r1[z] && r <= r2[z]}, {{z, -0.02, 0.02}, {r, 0,
      0.05}}];
RegionPlot[\[CapitalOmega], AspectRatio -> Automatic]
op = Laplacian[u[r, z], {r, z}];
\[CapitalGamma]1 = DirichletCondition[u[r, z] == Ur, r == r1[z]];
\[CapitalGamma]2 = DirichletCondition[u[r, z] == 0, r == r2[z]];
sol = NDSolve[{op == 0, \[CapitalGamma]1, \[CapitalGamma]2}, 
   u, {r, z} \[Element] \[CapitalOmega]];

Can anybody shed any light on this?

Donald

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