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
Applied Mathematics | Mathematics | Numerical Analysis and Computation
AMS Subject Classification
65N30, 65N15, 45K20
Wu, Haijun and Zhang, Zhimin, "Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?" (2006). Mathematics Research Reports. 38.