PARAMETRIC POLYNOMIAL PRESERVING RECOVERY ON MANIFOLDS
Guozhi Dong, Hailong Guo
SIAM JOURNAL ON SCIENTIFIC COMPUTING | SIAM PUBLICATIONS | Published : 2020
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..View full abstract
Awarded by German Research Foundation under Germany's Excellence Strategy: The Berlin Mathematics Research Center MATH+
The work of the first author was partially supported by the German Research Foundation under Germany's Excellence Strategy: The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689). The work of the second author was partially supported by the Andrew Sisson Fund of the University of Melbourne.