Enforcement of constraints and maximum principles in the variational multiscale method
Enforcement of constraints and maximum principles in the variational multiscale method
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DOI：
10.1016/j.cma.2009.09.019
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发表时间：
2009-01-01
影响因子：
7.2
通讯作者：
Sangalli, Giancarlo
中科院分区：
文献类型：
--
作者：
Evans, John A.;Hughes, Thomas J. R.;Sangalli, Giancarlo
我们提出了一个新的理论框架，强制执行的约束变分多尺度（VMS）分析。该理论首先提出了一个抽象的运营商的格式，随后专门为稳定的对流扩散方程。该方法大量借鉴了约束优化和凸优化的结果。精细尺度的精确表达式推导出的约束，拉格朗日乘子，和精细尺度绿色的功能变分导数。所描述的方法能够开发满足预定义属性的数值方法。基于VMS-inspired稳定化方法、弱强制Dirichlet边界条件、最大值原理和守恒约束，给出了求解定常对流扩散方程的一种实用有效的方法. (C)2009 Elsevier B. V.保留所有权利。
We present a new theoretical framework for the enforcement of constraints in variational multiscale (VMS) analysis. The theory is first presented in an abstract operator format and subsequently specialized for the steady advection-diffusion equation. The approach borrows heavily from results in constrained and convex optimization. An exact expression for the fine-scales is derived in terms of variational derivatives of the constraints, Lagrange multipliers, and a fine-scale Green's function. The methodology described enables the development of numerical methods which satisfy predefined attributes. A practical and effective procedure for solving the steady advection-diffusion equation is presented based on a VMS-inspired stabilized method, weakly enforced Dirichlet boundary conditions, and enforcement of a maximum principle and conservation constraint. (C) 2009 Elsevier B.V. All rights reserved.