A Duality-Based Optimization Approach for Model Adaptivity in Heterogeneous Multiscale Problems

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.

MSC codes

  1. finite element method
  2. mesh adaptation
  3. model optimization
  4. model adaptation
  5. goal-oriented adaptivity
  6. DWR method

MSC codes

  1. 35J15
  2. 65C20
  3. 65N12
  4. 65N15
  5. 65N30
  6. 65N50

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Published In

cover image Multiscale Modeling & Simulation
Multiscale Modeling & Simulation
Pages: 412 - 428
ISSN (online): 1540-3467

History

Submitted: 29 November 2016
Accepted: 29 November 2017
Published online: 1 March 2018

MSC codes

  1. finite element method
  2. mesh adaptation
  3. model optimization
  4. model adaptation
  5. goal-oriented adaptivity
  6. DWR method

MSC codes

  1. 35J15
  2. 65C20
  3. 65N12
  4. 65N15
  5. 65N30
  6. 65N50

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