Document Type
Technical Report
Abstract
We study adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Secondly, we demonstrate by numerical examples that an adaptive procedure with a posteriori error estimator based on PPR does produce adaptive meshes satisfy our mesh density assumption, and the recovered gradient by PPR is indeed supercoveregent in the adaptive process.
Number in Series
2006.08
Disciplines
Applied Mathematics | Mathematics | Numerical Analysis and Computation
AMS Subject Classification
65N30, 65N15, 45K20
Recommended Citation
Wu, Haijun and Zhang, Zhimin, "Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?" (2006). Mathematics Research Reports. 38.
https://digitalcommons.wayne.edu/math_reports/38
Comments
This research is supported in part by China NSF under the grant 10401016 and by the National Basic Research Program under the Grant 2005CB321701, and in part by the US National Science Foundation grant DMS-0031807.