Understanding Boundary integration for L2 Spaces

[AlejandroMunozManterola]

Understanding Boundary integration for L2 Spaces

[najlkin]

Hi, what you observe is a totally correct behavior. The key is to understand how L2 elements work. Unlike continuous elements, L2 elements are not precisely defined at boundaries of elements and the notion of trace is used instead, which is not defined uniquely and different common choices exist. Practically, this means "open" bases are used for them typically, like the default Gauss-Legendre, which do not have DOFs at the boundaries. This implies that all DOFs essentially contribute to interpolation of the values (even though we may expect the closest contribute the most). This is the reason why the integration is performed on the whole element.

Projection to H1 might be an option, but keep in mind it is a global procedure, so it is a kind of integral fitting. This might cause artificial dislocation of some values, which might or might not be welcomed depending on the application (i.e., do you expect continuous or discontinuous profiles?). I would try to think differently maybe, I do not know your application exactly, but cannot you reformulate the problem in the weak sense? Like instead of calculation of strong divergence/curl, calculate them weakly? That is how L2 elements are typically used in EM codes 😉