Online basis construction for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method
It addresses the need for efficient adaptive multiscale methods for flow problems in heterogeneous media, but the contribution is incremental as it extends existing online enrichment techniques to goal-oriented adaptivity.
The paper develops an online enrichment framework for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method for flow problems in heterogeneous media, proposing three primal-dual based strategies. Numerical experiments demonstrate efficiency for high-contrast heterogeneous problems.
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.