Unfitted finite elements approach from Deckelnick / Eliott / Dziuk paper
imajna.oxfordjournals.org/cgi/reprint/drn049v1.pdf
This paper describes almost the same approach that we are using - obtaining solution on surface by extending to unfitted mesh containing h-narrow band around the surface.
Only difference seems that they are using orthogonal projection from earlier Dziuk's paper to extend the domain, and they do mention Greer's idea as well.
In essence, the unfitted mesh is restricted to a fitted mesh. Elements that fall across the boundary level sets are chopped to only the part inside the band. This creates problems when the restricted triangle comes out very small or narrow.
In the paper, diagonal preconditioning is used. Here are my convergence results with no preconditioning:
imajna.oxfordjournals.org/cgi/reprint/drn049v1.pdf
This paper describes almost the same approach that we are using - obtaining solution on surface by extending to unfitted mesh containing h-narrow band around the surface.
Only difference seems that they are using orthogonal projection from earlier Dziuk's paper to extend the domain, and they do mention Greer's idea as well.
In essence, the unfitted mesh is restricted to a fitted mesh. Elements that fall across the boundary level sets are chopped to only the part inside the band. This creates problems when the restricted triangle comes out very small or narrow.
In the paper, diagonal preconditioning is used. Here are my convergence results with no preconditioning:
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