Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4613804 | Journal of Mathematical Analysis and Applications | 2017 | 25 Pages |
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
Authors
Wen-ming He, Junzhi Cui, Jiangman Shen,