TY - JOUR
T1 - Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity
AU - Cao, X.
AU - Mitra, K.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - We analyze a fully discrete numerical scheme for the model describing two-phase immiscible flow in porous media with dynamic effects in the capillary pressure. We employ the Euler implicit method for the time discretization. The spatial discretization is based on the mixed finite element method (MFEM). Specifically, the lowest order Raviart–Thomas elements are applied. In this paper, the error estimates for the saturation, fluxes and phase pressures in L
∞ (0,T;L
2 (Ω)) are derived for the temporal and spatial discretization to show the convergence of the scheme. Finally, we present some numerical results to support the theoretical findings.
AB - We analyze a fully discrete numerical scheme for the model describing two-phase immiscible flow in porous media with dynamic effects in the capillary pressure. We employ the Euler implicit method for the time discretization. The spatial discretization is based on the mixed finite element method (MFEM). Specifically, the lowest order Raviart–Thomas elements are applied. In this paper, the error estimates for the saturation, fluxes and phase pressures in L
∞ (0,T;L
2 (Ω)) are derived for the temporal and spatial discretization to show the convergence of the scheme. Finally, we present some numerical results to support the theoretical findings.
KW - Dynamic capillary pressure
KW - Euler implicit method
KW - Immiscible two-phase flow
KW - Mixed finite elements
UR - http://www.scopus.com/inward/record.url?scp=85059822306&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2018.12.022
DO - 10.1016/j.cam.2018.12.022
M3 - Article
SN - 0377-0427
VL - 353
SP - 164
EP - 178
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -