We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and a realization of it in one space dimension which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines: one hinges on Binev's algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy; the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying Doerfler marking and h-refinement.
|Titolo:||An adaptive hp-DG-FE Method for Elliptic Problems. Convergence and Optimality in the 1D Case|
|Data di pubblicazione:||Being printed|
|Appare nelle tipologie:||1.1 Articolo in rivista|