Here the draft of gradient jump penalty according to Rodrigo et. al. (2021) is initially performed. The whole thing seems to act on the weak form equation in a seemly correctly way. However, the key point is to deal with the vertices points/edges has more than 2 neighbouring elements, which seemly could not be issued by field_t and its gsop. Moreover, the quantity on the same spatial point may have different values when it's associated to different facets, which also requires a new type containing data array of size (lx, lx, 6, nelv) for hexahedral elements and its corresponding gather-scatter operations. And a consideration with long future extension: how to extend the code for tetrahedral mesh?
Here the draft of gradient jump penalty according to Rodrigo et. al. (2021) is initially performed. The whole thing seems to act on the weak form equation in a seemly correctly way. However, the key point is to deal with the vertices points/edges has more than 2 neighbouring elements, which seemly could not be issued by field_t and its gsop. Moreover, the quantity on the same spatial point may have different values when it's associated to different facets, which also requires a new type containing data array of size (lx, lx, 6, nelv) for hexahedral elements and its corresponding gather-scatter operations. And a consideration with long future extension: how to extend the code for tetrahedral mesh?