First: Thank you for the fixes!
After some trial and error work the assembling for special differential equations, seems to be working as well.
Now I am am trying to understand the behavior of the interpolation error a bit better. I compare CoefficientFunctions projected on the L2 space (3D) and ProlongateCoefficientFunctions(1D+2D) first projected into the tensor product space and then into the L2. For that I have two questions for understanding the evaluation of coefficient functions in the tp space:
1. Does the line
Code:
CoefficientFunction->Evaluate(MapedIntegrationRule,Matrix);
especially
Code:
cfstd->Evaluate(tpmir,result);
give me the evaluation of the CoefficientFunction in the mapped interpolation points? Or rather some coefficients for the basis functions corresponding to the integration rule (and therefore some interpolation)?
2. I am a bit confused about what's going on in TransferToTPMesh. I interpret the lines 678 to 687 as something like
elmatout = A^{-1} A_2^{-T}A^T resultasmat B B^{-1} B_2^{-T}
which means
elmatout = A^{-1} A_2^{-T}A^T resultasmat B_2^{-T}
for
A = shapesx, A_2 = shapesx2,
B = shapesy, B_2 = spapesy2.
Was there transposing intentionally left out or did I misinterpret the CalcInverse?