Abstract
We review two multiscale finite-element methods, the mixed multiscale finite-element method [Chen and Hou, 2002; Aarnes, 2004] and the numerical subgrid upscaling method [Arbogast et al., 1998; Arbogast, 2000, 2002], and demonstrate some of their shortcomings. We then show that combining ideas from both methods yields a new approach that is less likely to suffer from the shortcomings of the original methods. The performance of the new approach is demonstrated by a few numerical experiments