Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

The $ W^1_p$ stability of the Ritz projection on graded meshes


Author: Hengguang Li
Journal: Math. Comp. 86 (2017), 49-74
MSC (2010): Primary 65N30, 65N12
DOI: https://doi.org/10.1090/mcom/3101
Published electronically: April 13, 2016
MathSciNet review: 3557793
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Consider the Poisson equation on a convex polygonal domain and the finite element method of degree $ m\geq 1$ associated with a family of graded meshes for possible singular solutions. We prove the stability of the Ritz projection onto the finite element space in $ W^1_p$, $ 1<p\leq \infty $. Consequently, we obtain finite element error estimates in $ W^1_p$ for $ 1<p\leq \infty $ and in $ L^p$ for $ 1<p<\infty $. The key to the analysis is the use of the ``index engineering'' methodology in modified Kondrat$ '$ev weighted spaces. We also mention possible extensions and applications of these results.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N12

Retrieve articles in all journals with MSC (2010): 65N30, 65N12


Additional Information

Hengguang Li
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: hli@math.wayne.edu

DOI: https://doi.org/10.1090/mcom/3101
Received by editor(s): June 5, 2014
Received by editor(s) in revised form: October 31, 2014, and June 18, 2015
Published electronically: April 13, 2016
Additional Notes: The author was supported in part by the NSF Grants DMS-1158839, DMS-1418853, and by the Wayne State University Grants Plus Program.
Article copyright: © Copyright 2016 American Mathematical Society