Goal-oriented error estimation and adaptivity in MsFEM computations

We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In previous work, we have shown how to use, in MsFEM framework, concept of Constitutive Relation Error (CRE) obtain guaranteed and fully computable posteriori error estimate energy norm (as well as indicators on various sources). Here, CRE is coupled with solution an adjoint problem control drive adaptive procedure respect given output interest. Furthermore, local non-intrusive enrichment technique proposed enhance accuracy bounds. The overall strategy, which automatic robust, enables reach appropriate trade-off between certified reliability computational cost context. performances method are investigated several illustrative numerical test cases. particular, estimation observed be very accurate, yielding efficient procedure.