A best approximation evaluation of a finite element calculation Original Research Article

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