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Online basis construction for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method (1812.02290v2)
Published 6 Dec 2018 in math.NA
Abstract: In this research, we develop an online enrichment framework for goal-oriented adaptivity within the generalized multiscale finite element method for flow problems in heterogeneous media. The method for approximating the quantity of interest involves construction of residual-based primal and dual basis functions used to enrich the multiscale space at each stage of the adaptive algorithm. Three different online enrichment strategies based on the primal-dual online basis construction are proposed: standard, primal-dual combined and primal-dual product based. Numerical experiments are performed to illustrate the efficiency of the proposed methods for high-contrast heterogeneous problems.