Reduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations: A Penalty Approach

机译：减少基础的一个前后误差界限，用于方程式：惩罚方法

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We present reduced basis approximations and associated rigorous a posteriori error bounds for the instationary Stokes equations. The proposed method is an extension of the penalty approach introduced in Gerner and Veroy (2011b) to the time-dependent setting: The introduction of a penalty term enables us to develop a posteriori error bounds that do not rely on the expensive calculation of inf-sup stability constants and that are thus computationally very efficient. Numerical results show the rapid convergence of reduced basis approximations and demonstrate the effects of the penalty parameter.

机译：我们提出了减少的基础近似和相关的严格对阵方程的后验误差界限。所提出的方法是在吉伦和VENER（2011B）中引入的惩罚方法的延伸，以时间依赖的设置：惩罚术语的引入使我们能够开发一个不依赖于昂贵的INF的昂贵计算的后验误差界限支持稳定性常数，因此计算地非常有效。数值结果表明，减少基础近似的快速收敛性，并证明了惩罚参数的影响。

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《Vienna International Conference on Mathematical Modelling》|2013年||共6页
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Anna-Lena Gerner; Karen Veroy;
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中图分类 TP15-53;
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Saddle point problem; Stokes equations; Incompressible fluid flow; Model order reduction; Reduced basis method; Penalty; A posteriori error bounds;

机译：马鞍点问题;斯托克斯方程;不可压缩的流体流动;模型顺序减少;减少基础方法;惩罚;一个后验错误界限;

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专利

1. Reduced basis a posteriori error bounds for the stokes equations in parametrized domains: A penalty approach [J] . Gerner A.-L., Veroy K. Mathematical models and methods in applied sciences . 2011,第10期

机译：参数化域中斯托克斯方程的简化后验误差界：一种惩罚方法
2. Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds [J] . Veroy K, Patera AT International Journal for Numerical Methods in Fluids . 2005,第8a9期

机译：经认证的参数化稳定不可压缩Navier-Stokes方程的实时解决方案：严格的减少基后验误差界限
3. Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds [J] . Veroy K, Patera AT International Journal for Numerical Methods in Fluids . 2005,第8a9期

机译：经认证的参数化稳定不可压缩Navier-Stokes方程的实时解决方案：严格的减少基后验误差界限
4. Reduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations: A Penalty Approach [C] . Anna-Lena Gerner, Karen Veroy Vienna International Conference on Mathematical Modelling . 2013

机译：减少基础的一个前后误差界限，用于方程式：惩罚方法
5. A posteriori finite element bounds: Application to outputs of the three-dimensional Navier-Stokes equations. [D] . Cheng, Zhong. 2003

机译：后验有限元界：应用于三维Navier-Stokes方程的输出。
6. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

机译：弱奇异积分方程的自适应IGA边界元方法的可靠高效后验误差估计
7. Reduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations [O] . Gerner, Anna-Lena, Reusken, Arnold, Veroy, Karen 2012

机译：减少基础的实证stokes的后验误差界限方程

Reduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations: A Penalty Approach

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