One-sided approximation and variational inequalities
Umberto Mosco, Gilbert Strang · Bulletin of the American Mathematical Society · 1974
For piecewise linear approximation of the unilateral Laplace equation (also known as the obstacle problem, and governed by a variational inequality), we prove that the gradient of the error u-u h is of order h.The proof rests on approximation of nonnegative functions U by nonnegative splines V h ^U. AMS (MOS) subject classifications (1970). Primary 35J20, 65N30, 41A15.