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The finite volume method based on the Crouzeix–Raviart element for a fracture model
Author(s) -
Chen Shuangshuang,
Li Xiaoli,
Rui Hongxing
Publication year - 2019
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.22384
Subject(s) - mathematics , piecewise , finite element method , uniqueness , fracture (geology) , constant (computer programming) , matrix (chemical analysis) , extended finite element method , finite volume method , mathematical analysis , mixed finite element method , mechanics , geotechnical engineering , geology , materials science , physics , thermodynamics , computer science , composite material , programming language
Abstract In this paper, we present and analyze a finite volume method based on the Crouzeix–Raviart element for the coupled fracture model, where the fluid flow is governed by Darcy's law in the one‐dimensional fracture and two‐dimensional surrounding matrix. In the numerical scheme, the pressure in the matrix and fracture is respectively approximated by the Crouzeix–Raviart elements and piecewise constant functions, and then the velocity is calculated by piecewise constant functions element by element. The existence and uniqueness of the numerical solution are discussed, and optimal order error estimates for both the pressure p and the velocity u are proved on general triangulations. We finally carry out numerical experiments, and results confirm our theoretical analysis.