ufl.log.UFLException: Cannot determine geometric dimension from expression

Please make sure that your code reproduces the error message when copy-pasting it into a new file.
You are missing several key definitions, such as a mesh (can be a built in one such as a UnitSquareMesh) and the variables theta and r. Note that you can remove the line solve(a==L, w, bcs), as the code is only dependent on the split of w, not the actual values.

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