|Title:|| Convergence and Optimality of hp-AFEM|
|Date:|| Wednesday 18th March 2015|
|Author(s) :|| Canuto, C.; Nochetto, R.h.; Stevenson R,; Verani, M.|
|Abstract:|| We design and analyze an adaptive hp-finite element method
(hp-AFEM) in dimensions $n=1,2$.
The algorithm consists of iterating two routines:
HP-NEARBEST finds a near-best hp-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
hp-approximation, and acts as a coarsening step. We prove
convergence and instance optimality.