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maybe a trivial question, but how is grad(u) for u being a P1 function defined on the mesh edges (since it might be discontinuous), especially when evaluating at the nodes?
gradients are always evaluated element-wise.
when you say grad(u), distributional parts (i.e. jumps across edges) are ignored.
the gradient is a discontinuous function, it has different values on different elements connected to a vertex.
