Fully discrete mixed finite element approximations for non-Darcy flows in porous media

M. Y. Kim; E. J. Park

doi:10.1016/S0898-1221(99)00291-6

Fully discrete mixed finite element approximations for non-Darcy flows in porous media

M. Y. Kim, E. J. Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

A numerical approximation procedure is proposed to solve equations describing non-Darcy flow of a single-phase fluid in a porous medium in two or three spacial dimensions, including the generalized Forchheimer equation. Fully discrete mixed finite element methods are considered and analyzed for the approximation. Existence and uniqueness of the approximation are discussed and optimal order error estimates in L² are derived for the three relevant functions.

Original language	English
Pages (from-to)	113-129
Number of pages	17
Journal	Computers and Mathematics with Applications
Volume	38
Issue number	11
DOIs	https://doi.org/10.1016/S0898-1221(99)00291-6
Publication status	Published - 1999 Dec

Bibliographical note

Funding Information:
*The research of this author was supported in part by a post-doctoral fellowship from the University of Trento, Italy. ?The research of this author was supported in part by G.N.A.F.A. of C.N.R. (Italy) and KOSEF #97070101013 (Korea).

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/S0898-1221(99)00291-6

Cite this

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abstract = "A numerical approximation procedure is proposed to solve equations describing non-Darcy flow of a single-phase fluid in a porous medium in two or three spacial dimensions, including the generalized Forchheimer equation. Fully discrete mixed finite element methods are considered and analyzed for the approximation. Existence and uniqueness of the approximation are discussed and optimal order error estimates in L2 are derived for the three relevant functions.",

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AU - Kim, M. Y.

AU - Park, E. J.

N1 - Funding Information: *The research of this author was supported in part by a post-doctoral fellowship from the University of Trento, Italy. ?The research of this author was supported in part by G.N.A.F.A. of C.N.R. (Italy) and KOSEF #97070101013 (Korea).

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Y1 - 1999/12

N2 - A numerical approximation procedure is proposed to solve equations describing non-Darcy flow of a single-phase fluid in a porous medium in two or three spacial dimensions, including the generalized Forchheimer equation. Fully discrete mixed finite element methods are considered and analyzed for the approximation. Existence and uniqueness of the approximation are discussed and optimal order error estimates in L2 are derived for the three relevant functions.

AB - A numerical approximation procedure is proposed to solve equations describing non-Darcy flow of a single-phase fluid in a porous medium in two or three spacial dimensions, including the generalized Forchheimer equation. Fully discrete mixed finite element methods are considered and analyzed for the approximation. Existence and uniqueness of the approximation are discussed and optimal order error estimates in L2 are derived for the three relevant functions.

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ER -

Fully discrete mixed finite element approximations for non-Darcy flows in porous media

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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