A priori estimates for two multiscale finite element methods using multiple global fields to wave equations

Lijian Jiang*, Yalchin Efendiev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider a scalar wave equation with nonseparable spatial scales. If the solution of the wave equation smoothly depends on some global fields, then we can utilize the global fields to construct multiscale finite element basis functions. We present two finite element approaches using the global fields: partition of unity method and mixed multiscale finite element method. We derive a priori error estimates for the two approaches and theoretically investigate the relation between the smoothness of the global fields and convergence rates of the approximations for the wave equation.

Original languageEnglish (US)
Pages (from-to)1869-1892
Number of pages24
JournalNumerical Methods for Partial Differential Equations
Volume28
Issue number6
DOIs
StatePublished - Nov 1 2012

Keywords

  • a priori error estimates
  • mixed multiscale finite element method
  • partition of unity method
  • wave equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics
  • Analysis

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