Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates

被引：29
|
作者：
Buffa, Annalisa [1 ]
Giannelli, Carlotta [2 ]
机构：
[1] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland
[2] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67a, I-50134 Florence, Italy
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2017年 / 27卷 / 14期
关键词：
Isogeometric analysis; hierarchical splines; adaptivity; SUITABLE T-SPLINES; FINITE-ELEMENT METHODS; LINEAR INDEPENDENCE; LOCAL REFINEMENT; SPACES; DEFINITION;
D O I：
10.1142/S0218202517500580
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and continue the study of its numerical properties. We prove that our AIGM is optimal in the sense that delivers optimal convergence rates as soon as the solution of the underlying partial differential equation belongs to a suitable approximation class. The main tool we use is the theory of adaptive methods, together with a local upper bound for the residual error indicators based on suitable properties of a well selected quasi-interpolation operator on hierarchical spline spaces.
引用
收藏
页码：2781 / 2802
页数：22
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