Journal of Scientific Computing

, Volume 60, Issue 3, pp 505–536 | Cite as

Coupled Model and Grid Adaptivity in Hierarchical Reduction of Elliptic Problems

  • Simona Perotto
  • Alessandro Veneziani


In this paper we propose a surrogate model for advection–diffusion–reaction problems characterized by a dominant direction in their dynamics. We resort to a hierarchical model reduction where we couple a modal representation of the transverse dynamics with a finite element approximation along the mainstream. This different treatment of the dynamics entails a surrogate model enhancing a purely 1D description related to the leading direction. The coefficients of the finite element expansion along this direction introduce a generally non-constant description of the transversal dynamics. Aim of this paper is to provide an automatic adaptive approach to locally select the dimension of the modal expansion as well as the finite element step in order to satisfy a prescribed tolerance on a goal functional of interest.


Model reduction A posteriori modeling error analysis Mesh adaptivity Domain decomposition Finite elements 



The authors wish to thank warmly Alexandre Ern for many discussions and fundamental suggestions he gave along the entire preparation of the manuscript.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.MOX, Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanItaly
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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