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.

An adaptive hp-DG-FE Method for Elliptic Problems. Convergence and Optimality in the 1D Case / Antonietti, Paola; Canuto, Claudio; Verani, Marco. - In: COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION. - ISSN 2096-6385. - ELETTRONICO. - 1:(2019), pp. 309-331. [10.1007/s42967-019-00026-9]

An adaptive hp-DG-FE Method for Elliptic Problems. Convergence and Optimality in the 1D Case

Claudio Canuto;
2019

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2724949