A posteriori error estimation for the steady Navier-Stokes equations in random domains
A posteriori error estimation for the steady Navier-Stokes equations in random domains
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DOI：
10.1016/j.cma.2016.10.008
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发表时间：
2017-01-01
影响因子：
7.2
通讯作者：
Picasso, Marco
中科院分区：
文献类型：
--
作者：
Guignard, Diane;Nobile, Fabio;Picasso, Marco
本文考虑定常不可压Navier-Stokes方程的有限元误差近似，该方程定义在一个小扰动随机扰动区域上。引入随机映射，将这些方程转化为固定参考域上的随机系数偏微分方程。在随机映射和输入数据的适当假设下，特别是所谓的小数据假设下，我们证明了问题的适定性。然后，我们假设的映射依赖于affafferly L独立的随机变量，并采取扰动的方法，扩大解决方案相对于一个小参数，控制量的随机性的问题。我们进行了一个后验误差分析的一阶近似误差，即精确（随机）的解决方案和有限元近似的第一项的扩展相对于a之间的误差。数值结果说明了理论结果和误差估计的有效性。(C)2016爱思唯尔B. V.保留所有权利。
We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed reference domain with random coefficients. Under suitable assumptions on the random mapping and the input data, in particular the so-called small data assumption, we prove the well-posedness of the problem. We assume then that the mapping depends affinely on L independent random variables and adopt a perturbation approach expanding the solution with respect to a small parameter a that controls the amount of randomness in the problem. We perform an a posteriori error analysis for the first order approximation error, namely the error between the exact (random) solution and the finite element approximation of the first term in the expansion with respect to a. Numerical results are given to illustrate the theoretical results and the effectiveness of the error estimators. (C) 2016 Elsevier B.V. All rights reserved.