论文标题
稳定的有限元方法，用于对流扩散方程。 II：以对流为主的制度
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. II: convection-dominated regime
论文作者
论文摘要
我们考虑了固定对流扩散方程不足的数据同化问题的数值近似，并在[Numer中扩展了我们先前的分析。数学。 144，451--477，2020]到对流为主的制度。稍微调整提出主要扩散的稳定有限元方法，我们利用局部误差分析，通过数据集获得对流场特征的准最佳收敛。重量功能乘以离散解决方案为Lipschitz，并证明相应的超近似结果（离散换向属性）。数据扰动的效果包括在分析中，我们通过一些数值实验总结了本文。
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [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 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.
