TY - JOUR
T1 - Analysis of fully discrete FEM for miscible displacement in porous media with Bear–Scheidegger diffusion tensor
AU - Cai, Wentao
AU - Li, Buyang
AU - Lin, Yanping
AU - Sun, Weiwei
PY - 2019/2/28
Y1 - 2019/2/28
N2 - Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear–Scheidegger diffusion–dispersion tensor: D(u)=γdmI+|u|(αTI+(αL-αT)u⊗u|u|2).Previous works on optimal-order L ∞ (0 , T; L 2 ) -norm error estimate required the regularity assumption ∇ x ∂ t D(u(x, t)) ∈ L ∞ (0 , T; L ∞ (Ω)) , while the Bear–Scheidegger diffusion–dispersion tensor is only Lipschitz continuous even for a smooth velocity field u. In terms of the maximal L p -regularity of fully discrete finite element solutions of parabolic equations, optimal error estimate in L p (0 , T; L q ) -norm and almost optimal error estimate in L ∞ (0 , T; L q ) -norm are established under the assumption of D(u) being Lipschitz continuous with respect to u.
AB - Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear–Scheidegger diffusion–dispersion tensor: D(u)=γdmI+|u|(αTI+(αL-αT)u⊗u|u|2).Previous works on optimal-order L ∞ (0 , T; L 2 ) -norm error estimate required the regularity assumption ∇ x ∂ t D(u(x, t)) ∈ L ∞ (0 , T; L ∞ (Ω)) , while the Bear–Scheidegger diffusion–dispersion tensor is only Lipschitz continuous even for a smooth velocity field u. In terms of the maximal L p -regularity of fully discrete finite element solutions of parabolic equations, optimal error estimate in L p (0 , T; L q ) -norm and almost optimal error estimate in L ∞ (0 , T; L q ) -norm are established under the assumption of D(u) being Lipschitz continuous with respect to u.
UR - http://www.scopus.com/inward/record.url?scp=85062631179&partnerID=8YFLogxK
U2 - 10.1007/s00211-019-01030-0
DO - 10.1007/s00211-019-01030-0
M3 - Journal article
AN - SCOPUS:85062631179
SN - 0029-599X
VL - 141
SP - 1009
EP - 1042
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 4
ER -