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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Applications of the pseudo residual-free bubbles to the stabilization of the convection-diffusion-reaction problems in 2D
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Applications of the pseudo residual-free bubbles to the stabilization of the convection-diffusion-reaction problems in 2D

机译：伪无残留气泡在二维对流扩散反应问题稳定化中的应用

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摘要

A stabilized finite element method is studied herein for two-dimensional convection-diffusion-reaction problems. The method is based on the residual-free bubbles (RFB) method. However we replace the RFB functions by their cheap, yet efficient approximations computed on a specially chosen subgrid, which retain the same qualitative behavior. Since the correct spot of subgrid points plays a crucial role in the approximation, it is important to determine their optimal locations, which we do it through a minimization process with respect to the L_1-norm. The resulting numerical method has similar stability features with the well-known stabilized methods in the literature for the whole range of problem parameters and this fact is also confirmed by numerical experiments.
机译：本文针对二维对流扩散反应问题研究了一种稳定的有限元方法。该方法基于无残留气泡（RFB）方法。但是，我们通过在特殊选择的子网格上计算出的便宜而有效的近似值来替换RFB函数，这些近似值保留了相同的定性行为。由于子网格点的正确位置在逼近中起着至关重要的作用，因此确定它们的最佳位置非常重要，我们可以通过对L_1范数进行最小化处理来实现。对于整个问题参数范围，所得的数值方法具有与文献中众所周知的稳定方法相似的稳定性特征，这一事实也通过数值实验得到了证实。

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