On the control volume finite element methods and their applications to multiphase flow | Zendy

Zhangxin Chen | Zendy

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On the control volume finite element methods and their applications to multiphase flow

Author(s) -

Zhangxin Chen

Publication year - 2006

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2006.1.689

Subject(s) - finite element method , finite volume method , discontinuous galerkin method , mixed finite element method , extended finite element method , control volume , mathematics , smoothed finite element method , piecewise linear function , mathematical analysis , galerkin method , finite element limit analysis , hp fem , spectral element method , partial differential equation , piecewise , mechanics , boundary knot method , physics , thermodynamics , boundary element method

In this paper we systematically review the control volume finite element (CVFE) methods for numerical solutions of second-order partial differential equations. Their relationships to the finite difference and standard (Galerkin) finite element methods are considered. Through their relationship to the finite differences, upstream weighted CVFE methods and the conditions on positive transmissibilities (positive flux linkages) are studied. Through their relationship to the standard finite elements, error estimates for the CVFE are obtained. These estimates are comparable to those for the standard finite element methods using piecewise linear elements. Finally, an application to multiphase flows in porous media is presented.

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