Article ID Journal Published Year Pages File Type
4613804 Journal of Mathematical Analysis and Applications 2017 25 Pages PDF
Abstract

In this paper, we investigate the local ultraconvergence of k  -degree (k≥3)(k≥3) finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes ThTh 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,∂D), dist(x,M)dist(x,∂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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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