A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems

Matthias Maier, Rolf Rannache

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)412-428
Number of pages17
JournalMultiscale Modeling and Simulation
Volume16
Issue number1
DOIs
StatePublished - 2018

Keywords

  • DWR method
  • Finite element method
  • Goal-oriented adaptivity
  • Mesh adaptation
  • Model adaptation
  • Model optimization

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