Multiscale methods for parabolic equations with continuum spatial scales

Lijian Jiang*, Yalchin Efendiev, Victor Ginting

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper, we consider multiscale approaches for solving parabolic equations with heterogeneous coefficients. Our interest stems from porous media applications and we assume that there is no scale separation with respect to spatial variables. To compute the solution of these multiscale problems on a coarse grid, we define global fields such that the solution smoothly depends on these fields. We present various finite element discretization techniques and provide analyses of these methods. A few representative numerical examples are presented using heterogeneous fields with strong non-local features. These numerical results demonstrate that the solution can be captured more accurately on the coarse grid when some type of limited global information is used.

Original languageEnglish (US)
Pages (from-to)833-859
Number of pages27
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume8
Issue number4
DOIs
StatePublished - Jan 1 2007

Keywords

  • Continuum scale
  • Global information
  • Multiscale methods
  • Parabolic equations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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