Mixed multiscale finite element methods using limited global information

J. E. Aarnes, Y. Efendiev, L. Jiang

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

Abstract

In this paper, we present a mixed multiscale finite element method using limited global information. We consider a general case where multiple global information is given such that the solution depends smoothly on these global fields. The global fields typically contain smallscale (local or global) information required for achieving a convergence with respect to the coarse mesh size. We present a rigorous analysis and show that the proposed mixed multiscale finite element methods converge. Some preliminary numerical results are shown. We study a parameter dependent permeability field (a simplified case for general stochastic permeability fields). As for spatial heterogeneities, channelized permeability fields with strong nonlocal effects are considered. Using a few global fields corresponding to realizations of permeability fields, we show that one can achieve high accuracy in numerical simulations.

Original languageEnglish (US)
Pages (from-to)655-676
Number of pages22
JournalMultiscale Modeling and Simulation
Volume7
Issue number2
DOIs
StatePublished - 2008
Externally publishedYes

Keywords

  • Elliptic
  • Finite element
  • Global
  • Heterogeneities
  • Multiscale
  • Parabolic
  • Upscaling

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Mixed multiscale finite element methods using limited global information'. Together they form a unique fingerprint.

Cite this