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Finite element methods for an acoustic well‐logging problem associated with a porous medium saturated by a two‐phase immiscible fluid
Author(s) -
Sheen Dongwoo
Publication year - 1993
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.1690090205
Subject(s) - inviscid flow , compressibility , uniqueness , boundary value problem , porous medium , finite element method , convergence (economics) , mathematics , domain (mathematical analysis) , mechanics , boundary (topology) , mathematical analysis , porosity , stability (learning theory) , phase (matter) , geology , physics , thermodynamics , geotechnical engineering , computer science , quantum mechanics , machine learning , economic growth , economics
A mathematical model is presented concerning wave propagation in a domain that arises in geophysical well‐logging problems. The domain consists of a borehole Ω f surrounded by a porous medium Ω p . Ω f is filled with a compressible inviscid fluid, and Ω p is saturated by a two‐phase immiscible fluid. Absorbing boundary conditions for artificial boundaries and boundary conditions on the interface between Ω f and Ω p are used. The existence and uniqueness theorems are stated for the resulting initial‐boundary value problem. Stability and convergence estimates for a finite element method are also studied. © 1993 John Wiley & Sons, Inc.