A Duality-Based Optimization Approach for Model Adaptivity in Heterogeneous Multiscale Problems Academic Article uri icon


  • 2018 Society for Industrial and Applied Mathematics. This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators that are derived in the general context of the dual weighted residual (DWR) method. Based on the optimization approach a postprocessing strategy is formulated that lifts the requirement of strict a priori knowledge about applicability and quality of effective models. This allows for the systematic, goal-oriented tuning of effective models with respect to a quantity of interest. The framework is tested numerically on elliptic diffusion problems with different types of heterogeneous, random coefficients, as well as an advection-diffusion problem with a strong microscopic, random advection field.

published proceedings

  • Multiscale Modeling & Simulation

author list (cited authors)

  • Maier, M., & Rannacher, R.

publication date

  • January 1, 2018 11:11 AM