A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime

Burman Erik; Nechita Mihai; Oksanen Lauri

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A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime

机译：一种稳定有限元方法，用于对流-扩散方程下的逆问题。二：以对流为主的制度

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We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in Burman et al. (Numer. Math. 144:451-477, 2020) to the convection-dominated regime. Slightly adjusting the stabilized finite element method proposed for dominant diffusion, we draw upon a local error analysis to obtain quasi-optimal convergence along the characteristics of the convective field through the data set. The weight function multiplying the discrete solution is taken to be Lipschitz continuous and a corresponding super approximation result (discrete commutator property) is proven. The effect of data perturbations is included in the analysis and we conclude the paper with some numerical experiments.

机译：我们考虑了稳态对流-扩散方程的病态数据同化问题的数值近似，并将我们之前在Burman等人（Numer. Math. 144：451-477， 2020）中的分析扩展到对流主导的制度。对主导扩散的稳定有限元方法稍作调整，利用局部误差分析，通过数据集获得沿对流场特性的准最优收敛。将离散解相乘的权函数取为Lipschitz连续，并证明了相应的超近似结果（离散换向器性质）。分析中包括了数据扰动的影响，并通过一些数值实验结束了本文。

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来源
《Numerische Mathematik》 |2022年第3期|769-801|共33页
作者
Burman Erik; Nechita Mihai; Oksanen Lauri;
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UCL;

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正文语种英语
中图分类数值分析;
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NONCOERCIVE;

机译：非强制性;

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A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime

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