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Langrange Quadratic FieldShape Incorrect for Triangles
The hasNodesIn function for LagrangeQuadratic returns results that are inconsistent with the EntityShape it returns from getEntityShape. The problem is hasNodesIn says there are nodes on dimension 2 entities, but getEntityShape only special cases Quads. For triangles, it calls the QuadraticBase function, which returns a serendipity (only 6 nodes) triangle. This leads to problems with numberings/fields, because using hasNodesIn to skip over entities in loops doesn't work.
For my case, I can work around it by using SerendipityQuadratic.