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.

翻译：我们考虑了固定对流-扩散方程式中数据吸收不良问题的数字近似值,并将我们先前在[Numer. Math. 144, 451-477, 2020]中的分析扩展至对流主导制度。我们略微调整了为主要扩散而提出的固定的有限元素方法,利用当地误差分析,以通过数据集取得与对流领域特征的近似最佳趋同。离散解决方案的权重函数乘法是Libschitz,相应的超级近似结果(分光转换器属性)已被证明。数据扰动的效果被纳入了分析,我们用一些数字实验来完成论文。