For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart–Thomas and Brezzi–Douglas–Marini mixed finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to the local regularity of the solution. Several versions of the robust best approximations of the flux and the potential approximations are obtained. These robust and local optimal a priori estimates provide guidance for constructing robust a posteriori error estimates and adaptive methods for the mixed approximations.

中文翻译：

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低规则性的界面问题的鲁棒和局部最优先验误差估计：混合有限元逼近

对于可能具有非常低规则性的二维和三维椭圆界面问题，本文为Raviart-Thomas和Brezzi-Douglas-Marini混合有限元近似建立了先验误差估计。这些估计值相对于扩散系数是鲁棒的，并且相对于解的局部规律是最优的。获得了通量的鲁棒最佳近似和势近似的几种版本。这些鲁棒的和局部的最佳先验估计为构建鲁棒的后验误差估计和混合近似的自适应方法提供了指导。