Convergence and Optimality of hp-AFEM
Wednesday 18th March 2015
Canuto, C.; Nochetto, R.H.; Stevenson R,; Verani, M.
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.