Output Functional Control for Nonlinear Equations Driven by Anisotropic Mesh Adaption: The Navier--Stokes Equations
Output Functional Control for Nonlinear Equations Driven by Anisotropic Mesh Adaption: The Navier--Stokes Equations
复制标题
各向异性网格自适应驱动的非线性方程的输出函数控制：纳维-斯托克斯方程
DOI：
10.1137/070691930
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
S. Perotto
中科院分区：
文献类型：
--
作者：
S. Micheletti;S. Perotto
本文的贡献是双重的。首先，我们从著名的对偶加权残量(DWR)方法出发，建立了一个面向目标的非线性偏微分方程后验分析的理论框架，该框架考虑了原始问题和对偶问题的不同近似；从原始问题到对偶问题的不同的非齐次Dirichlet边界条件；数据逼近的误差；以及可能的镇定效应。其次，从这一框架出发，利用各向异性内插误差估计，设计了一种合理的各向异性网格自适应方法，用于连续分段线性有限元逼近N-S方程。所得到的自适应过程在一些相关的测试用例上得到了彻底的解决和验证。
The contribution of this paper is twofold. Firstly, moving from the very well-known dual-weighted residual (DWR) method, we set up a theoretical framework for a goal-oriented a posteriori analysis of nonlinear partial differential equations accounting for different approximations of the primal and dual problems; nonhomogeneous Dirichlet boundary conditions, even different on passing from the primal to the dual problem; the error due to data approximation; and the effect of a possible stabilization. Secondly, moving from this framework and employing anisotropic interpolation error estimates, a sound anisotropic mesh adaption procedure is devised for the numerical approximation of the Navier-Stokes equations by continuous piecewise linear finite elements. The resulting adaptive procedure is thoroughly addressed and validated on some relevant test cases.