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

作　　者：Paola Antonietti Claudio Canuto Marco Verani 

机构地区：[1]MOX-Dipartimento di Matematica,Politecnico di Milano,P.zza Leonardo Da Vinci 32,20133 Milan,Italy [2]Dipartimento di Scienze Matematiche,Politecnico di Torino,Corso Duca degli Abruzzi 24,10129 Turin,Italy

出　　处：《Communications on Applied Mathematics and Computation》2019年第3期309-331,共23页应用数学与计算数学学报（英文）

摘　　要：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 D?rfler marking and h refinement.

关 键 词：ELLIPTIC problem DISCONTINUOUS GALERKIN method HP-ADAPTIVITY CONVERGENCE and OPTIMALITY 

分 类 号：O1[理学—数学]