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A priori estimates for two multiscale finite element methods using multiple global fields to wave equations
Author(s) -
Jiang Lijian,
Efendiev Yalchin
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20706
Subject(s) - partition of unity , mathematics , finite element method , a priori and a posteriori , partial differential equation , wave equation , smoothness , mixed finite element method , mathematical analysis , scalar (mathematics) , convergence (economics) , scalar field , extended finite element method , geometry , physics , philosophy , epistemology , economics , mathematical physics , thermodynamics , economic growth
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. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011