Adaptive strategies

The success of local multiscale model reduction techniques strongly depends on the local adaptivity, which can guide the appropriate number of multiscale basis functions in each coarse block. To determine the number of basis functions, computable a-posteriori error indicators are needed. In this chapter, we present an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. We show it for continuous Galerkin formulation; however, this concept can be generalized to other discretizations. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high-contrast coefficients.