PARAMETRIC POLYNOMIAL PRESERVING RECOVERY ON MANIFOLDS

Abstract

This paper investigates gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds which have been assumed for some significant gradient recovery methods in the literature. Another advantage of PPPR is that superconvergence is guaranteed without the symmetric condition which is required in the existing techniques. As an application, we show its capability of constructing an asymptotically exact a posteriori error estimator. Several numerical examples on two-dimensional surfaces are presented to support the theoretical results, and comparisons with existi..