The local ultraconvergence for high-degree Galerkin finite element methods

In this paper, we investigate the local ultraconvergence of k-degree (k >= 3) finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes 77, on a bounded rectangular domain D. The k-degree finite element estimates are developed for the Green's function and its derivatives. They are employed to explore the relationship among dist(x, partial derivative D), dist(x, M) and the ultraconvergence of k-degree finite element methods at vertex x, where M is the set of corners of D. Numerical examples are conducted to demonstrate our theoretical results. (C) 2016 Elsevier Inc. All rights reserved.