We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, 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 Dörfler marking and h refinement.
Paola Antonietti, Claudio Canuto, Marco Verani
. An Adaptive hp-DG-FE Method for Elliptic Problems: Convergence and Optimality in the 1D Case[J]. Communications on Applied Mathematics and Computation, 2019
, 1(3)
: 309
-331
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DOI: 10.1007/s42967-019-00026-9
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