Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for “goal-oriented” adaptivity, the so-called Dual Weighted Residual (DWR) method. This allows for a systematic a posteriori balancing of multiscale modeling and discretization. The developed method is tested numerically at elliptic diffusion problems for different types of heterogeneous oscillatory coefficients.