Convergence and Optimality of hp-AFEM
Numerical Analysis
2015-03-16 v1
Abstract
We design and analyze an adaptive -finite element method (hp-AFEM) in dimensions . The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best -approximation of the current discrete solution and data to a desired accuracy, and REDUCE improves the discrete solution to a finer but comparable accuracy. The former hinges on a recent algorithm by Binev for adaptive -approximation, and acts as a coarsening step. We prove convergence and instance optimality.
Cite
@article{arxiv.1503.03996,
title = {Convergence and Optimality of hp-AFEM},
author = {Claudio Canuto and Ricardo H. Nochetto and Rob Stevenson and Marco Verani},
journal= {arXiv preprint arXiv:1503.03996},
year = {2015}
}