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Conservative flux recovery from the Q 1 conforming finite element method on quadrilateral grids
Author(s) -
Chou SoHsiang,
He Songnian,
Lin WenWei
Publication year - 2004
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.10084
Subject(s) - quadrilateral , discontinuous galerkin method , finite element method , mathematics , flux (metallurgy) , galerkin method , space (punctuation) , partial differential equation , order (exchange) , mathematical analysis , computer science , structural engineering , materials science , finance , economics , engineering , metallurgy , operating system
Compared with standard Galerkin finite element methods, mixed methods for second‐order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of the overall modeling processes. The purpose of this article is to introduce a direct method combining the standard Galerkin Q 1 conforming method with a cheap local flux recovery formula. The approximate flux resides in the lowest order Raviart‐Thomas space and retains local conservation property at the cluster level. A cluster is made up of at most four quadrilaterals. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 104–127, 2004