A priori error analysis for transient problems using Enhanced Velocity approach in the discrete-time setting

Abstract

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 for single phase flow and transport and demonstrated as mass conservative and efficient method. Numerical tests validating the backward Euler theory are presented. These error estimates are useful in the determining of time step size and the space discretization size.