A best approximation evaluation of a finite element calculation (Q1970449)

The authors discuss an electrostatics problem whose solution must in the set \(\Phi\) of all real \(n\times n\) symmetric matrices with all row sums equal to zero. With respect to the Frobenius norm, they provide an algorithm that finds the member of \(\Phi\) which is closest to any given \(n\times n\) matrix, and determines the distance between the two. This algorithm makes it practical to find the distances to \(\Phi\) of finite element approximate solutions of the electrostatics problem, and to reject those which are not sufficiently close.