Time discretization along with space discretization is important in the
numerical simulation of subsurface flow applications for long run. In this
paper, we derive theoretical convergence error estimates in discrete-time
setting for transient problems with the Dirichlet boundary condition. Enhanced
Velocity Mixed FEM as domain decomposition method is used in the space
discretization and the backward Euler method and the Crank-Nicolson method are
considered in the discrete-time setting. Enhanced Velocity scheme was used in
the adaptive mesh refinement dealing with heterogeneous porous media [1, 2] for
single phase flow and transport and demonstrated as mass conservative and
efficient method. Numerical tests validating the backward Euler theory are
presented. This error estimates are useful in the determining of time step size
and the space discretization size.
References.
[1] Yerlan Amanbek, Gurpreet Singh, Mary F Wheeler, and Hans van Duijn.
Adaptive numerical homogenization for upscaling single phase flow and
transport. ICES Report,12:17, 2017.
[2] Gurpreet Singh, Yerlan Amanbek, and Mary F Wheeler. Adaptive
homogenization for upscaling heterogeneous porous medium. In SPE Annual
Technical Conference and Exhibition. Society of Petroleum Engineers, 2017
