In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott--Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.

翻译：本文针对具有Robin型跳跃界面条件的达西流动问题，发展了混合有限元方法的可计算后验误差估计器。我们利用Stenberg后处理技术构建了能量范数型的后验误差估计器。通过采用界面适应的Helmholtz型分解和界面适应的Scott-Zhang型插值算子，证明了该估计器的可靠性。同时证明了后处理压力的局部有效性及可靠性。文中还给出了采用该估计器进行自适应算法数值模拟的结果。