Quasi-optimal convergence rate for an adaptive hybridizable discontinuous Galerkin method for Kirchhoff plates

被引：0

作者：

Sun, Pengtao ^{[3
]}

Huang, Xuehai ^{[1
,2
]}

机构：

[1] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China

[2] Wenzhou Univ, Dept Math, Wenzhou 325035, Peoples R China

[3] Univ Nevada Las Vegas, Dept Math Sci, 4505 Maryland Pkwy, Las Vegas, NV 89154 USA

来源：

NUMERISCHE MATHEMATIK | 2018年 / 139卷 / 04期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

A posteriori error estimates; Adaptive hybridizable C-0 discontinuous Galerkin method; Convergence; Computational complexity; Kirchhoff plate bending problems; FINITE-ELEMENT METHODS; POSTERIORI ERROR ESTIMATOR; PENALTY METHOD; MIXED METHODS; APPROXIMATIONS; REFINEMENT; ALGORITHM;

D O I：

10.1007/s00211-018-0953-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an adaptive hybridizable discontinuous Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a posteriori error estimator is produced for this HCDG method. Quasi-orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete Helmholtz decomposition. Based on these, the contraction property between two consecutive loops and complexity of the adaptive HCDG method are studied thoroughly. The key points in our analysis are a postprocessed normal-normal continuous bending moment from the HCDG method solution and a lifting of jump residuals from inter-element boundaries to element interiors.

引用

页码：795 / 829

页数：35

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