We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a posteriori error estimation. We introduce a hybrid mixed formulation with locally computable Lagrange multipliers and reconstruct the flux in the immersed Raviart-Thomas space. Based on this, we propose a new a posteriori error estimator that includes both volume and interface terms. We state its robust reliability and local efficiency, and validate the approach through numerical experiments.

翻译：本研究采用CutFEM方法，在非拟合网格上求解具有间断扩散系数的椭圆界面问题。主要贡献在于从CutFEM解重构保守通量，并将其应用于后验误差估计。我们引入具有局部可计算拉格朗日乘子的混合变分格式，并在浸入式Raviart-Thomas空间中重构通量。基于此，我们提出包含体积项与界面项的新型后验误差估计子，证明其具有鲁棒可靠性与局部有效性，并通过数值实验验证了该方法的有效性。