Details of Research Outputs

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. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.