From: John Peterson <peterson@cf...>  20050302 17:12:35

Currently, the Kelly Error Estimator ignores contributions to the residual coming from element sides on the boundary which have Neumann (flux) type boundary conditions such as grad(u).n = g on \Gamma_N I think it is reasonable to assume this error will be small, since the flux condition is enforced weakly during the formation of the element stiffness matrices. In the case of natural (flux=0) boundary conditions, it is common to not even add these terms to the stiffness matrix at all since they are assumed to be zero. My question is: would it be worth computing the boundary edge integrals \int g  grad(u_h).n^2 dS on the flux boundaries? My hunch is that in some applications, the estimator should actually be reporting a lot more error for the elements on the boundary than it currently is. In fact, I have seen actual evidence of this in a 2D tumorgrowth model with an exponential layer near the boundary. The row of elements closest to the boundary are not flagged for refinement even though several adjacent layers of elements are. What are your thoughts? The main implementation difficulty would be coming up with a general way to get the BCs and BC information into the error estimator without duplicating existing code in the matrix assembly routine. There are probably other issues as well. Any thoughts would be appreciated. John 