A NEW CLASS OF HIGHER ORDER MIXED FINITE VOLUME METHODS FOR ELLIPTIC PROBLEMS

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We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy's law, u = -kappa del p. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are equivalent to the nonconforming finite element spaces used to define them. The Darcy velocity can be locally recovered from the solution of nonconforming finite element method. Hence our work opens a way to make higher order mixed method more practicable. Three-dimensional extensions to parallelepiped elements are also presented. This work can be viewed as a generalization of earlier works which were devoted to reducing the (lowest order) mixed finite element method to a corresponding nonconforming finite element method. An optimal error analysis is carried out and numerical results are presented which confirm the theory.
Publisher
SIAM PUBLICATIONS
Issue Date
2012
Language
English
Article Type
Article
Keywords

ELEMENT METHODS; BOX-SCHEMES; GALERKIN METHODS; EQUATIONS; GRIDS

Citation

SIAM JOURNAL ON NUMERICAL ANALYSIS, v.50, no.4, pp.1941 - 1958

ISSN
0036-1429
DOI
10.1137/100812446
URI
http://hdl.handle.net/10203/102507
Appears in Collection
MA-Journal Papers(저널논문)
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