The K -Operator and the Qualocation Method for Strongly Elliptic Equations on Smooth Curves
Thanh Tran · Journal of Integral Equations and Applications · 1993
Superconvergence in L 2 -norm and max-norm is considered for the approximation of the equation Lu = f where L is a strongly elliptic pseudo-differential operator.Let u h be the qualocation approximation to the solution u.The K-operator applied to u h , by averaging the values of u h , achieves a better approximation than u h itself.In this way, we have exploited the highest order of convergence (in negative norm) available for u h to get high order convergence in L 2 and maximum estimates.The same result is obtained for the approximation of the derivatives of u.