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3

It seems increasing the number of requested points and the accuracy of NDSolve does the trick? rElectrode = 0.02; lElectrode = 0.6; lCamera = 1.5; rCamera = 1.5/2; voltage = 2.*10^4; domain = RegionDifference[ Rectangle[{-rCamera, -lCamera/2}, {rCamera, lCamera/2}], Rectangle[{-rElectrode, -lElectrode/2}, {rElectrode, lElectrode/2}]]; phi = ...

2

This is not a full answer but what I found so far… Following @user21's link If I use Method -> {"PDEDiscretization" -> {"FiniteElement", "MeshOptions" -> {"MaxCellMeasure" -> 0.0001}, "IntegrationOrder" -> 3}} as in P0 = NDSolveValue[{eqn0, DirichletCondition[P[R, z] == 0, R == 0], DirichletCondition[P[R, z] == 0, z == f[R]]}, ...

8

I'll mimic the precision/accuracy handling for FindRoot as indicated in its documentation: The default settings for AccuracyGoal and PrecisionGoal are WorkingPrecision/2. The setting for AccuracyGoal specifies the number of digits of accuracy to seek in both the value of the position of the root, and the value of the function at the root. The ...

2

As OP used in question f = BSplineFunction[data, SplineDegree -> 3, WorkingPrecision -> 8000] So WorkingPrecision is a very useful option in various numerical opertions. In this answer, I will give a function BSplineValue that owns the WorkingPrecision option. The definition of B-Spline curve \vec{C}(u)=\sum _{i=0}^n N_{i,p}(u) \vec{P}_i \qquad ...

2

I see at least two problems here: As written Prob1 is a List; you need to add // First (or similar) to extract a scalar value. You failed to define a starting value for Sh1 therefore Sh1 = 0 + Sh1 leads to an infinite recursion when the first scalar value is Equal to zero. Additionally some more improvements to be made: You should avoid starting user ...

6

Although BSplineFunction[] is sadly limited to machine precision results, it's not too hard in this case to make a function that will give exact results for exact input. You've already given the control points, so the task is a whole lot easier than the situation in this related answer. Just as in that answer, we use the strategy of starting with ...

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