Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis

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Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis

机译：广义Boussinesq问题的稳定有限元逼近：后验误差分析

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The purpose of this work is the design and analysis of a posteriori error estimators for low-order stabilized finite element approximations of a generalized Boussinesq problem. We consider standard stabilization procedures over conforming finite element spaces and a nonconforming one that delivers a divergence-free discrete velocity field. The analysis, that is valid for two and three-dimensional domains, relies on a smallness assumption on the solution and is based on a technique that involves the Ritz projection of the residuals. The devised a posteriori error estimators are proven to be globally reliable and locally efficient. Three dimensional numerical experiments reveal a competitive performance of adaptive procedures driven by the designed a posteriori error estimators. (C) 2019 Elsevier B.V. All rights reserved.

机译：这项工作的目的是为广义Boussinesq问题的低阶稳定有限元逼近设计和分析后验误差估计器。我们考虑在合格的有限元空间和不合格的空间上提供无散度离散速度场的标准稳定程序。该分析对二维和三维域有效，它依赖于解决方案的小假设，并且基于涉及残差的Ritz投影的技术。事实证明，设计的后验误差估计器在全球范围内都是可靠的，并且在本地有效。三维数值实验揭示了由设计后验误差估计器驱动的自适应程序的竞争性能。（C）2019 Elsevier B.V.保留所有权利。

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《Computer Methods in Applied Mechanics and Engineering》 |2020年第1期|112703.1-112703.25|共25页
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Univ Tecn Federico Santa Maria AM2V Av Espana 1680 Casilla 110-V Valparaiso Chile|Univ Tecn Federico Santa Maria Dept Matemat Av Espana 1680 Casilla 110-V Valparaiso Chile;

Univ Tecn Federico Santa Maria Dept Matemat Av Espana 1680 Casilla 110-V Valparaiso Chile;

Univ Tecn Federico Santa Maria AM2V Av Espana 1680 Casilla 110-V Santiago Chile|Univ Tecn Federico Santa Maria Dept Matemat Av Espana 1680 Casilla 110-V Santiago Chile;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
A generalized Boussinesq problem; Stabilized finite element methods; A posteriori error analysis; Adaptive finite elements;

机译：广义的Boussinesq问题;稳定的有限元方法;后验误差分析;自适应有限元;

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专利

1. A posteriori error estimators for stabilized finite element approximations of an optimal control problem [J] . Allendes Alejandro, Otarola Enrique, Rankin Richard Computer Methods in Applied Mechanics and Engineering . 2018,第OCTa1期

机译：最优控制问题的稳定有限元逼近的后验误差估计
2. A Posteriori Error Analysis of a Mixed-Primal Finite Element Method for the Boussinesq Problem with Temperature-Dependent Viscosity [J] . Almonacid Javier A., Gatica Gabriel N., Oyarzua Ricardo Journal of Scientific Computing . 2019,第2期

机译：具有温度依赖性粘度的Boussinesq问题的混合本原有限元方法的后验误差分析
3. A posteriori error analysis for finite element approximations of parabolic optimal control problems with measure data [J] . Shakya Pratibha, Sinha Rajen Kumar Applied numerical mathematics . 2019,第FEBa期

机译：带测量数据的抛物线型最优控制问题的有限元逼近的后验误差分析
4. Unified Framework for an A Posteriori Error Analysis of Non-Standard Finite Element Approximations of H(curl)-Elliptic Problems [C] . C. Carstensen, Ronald H. W. Hoppe International Conference on Electromagnetics in Advanced Applications . 2009

机译：用于H（卷曲）的非标准有限元近似的后验误差分析的统一框架
5. Adaptive finite element approximation of the Black-Scholes equation based on residual-type a posteriori error estimators. [D] . Li, Huifang. 2009

机译：基于残差型后验误差估计量的Black-Scholes方程的自适应有限元逼近。
6. A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay [O] . Wansheng Wang, Lijun Yi, Aiguo Xiao -1

机译：时滞广义扩散方程全离散有限元法的后验误差估计。
7. A posteriori error estimators for stabilized finite element approximations of an optimal control problem [O] . Allendes, Alejandro, Otarola, Enrique, Rankin, Richard 2017

机译：稳定有限元的后验误差估计近似的最优控制问题
8. Feedback Finite Element Method with a Posteriori Error Estimation. Part 1. The Finite Element Method and Some Basic Properties of the A Posteriori Error Estimator. [R] . Babuska, I., Miller, A. 1984

机译：具有后验误差估计的反馈有限元方法。第1部分：后验误差估计的有限元方法和一些基本性质。

Stabilized finite element approximations for a generalized Boussinesq problem: A posteriori error analysis

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