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A priori error analysis for transient problems using enhanced velocity approach in the discrete-time setting. (English) Zbl 1458.76062
Summary: 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 [the authors et al., J. Comput. Phys. 387, 117–133 (2019; Zbl 1452.76080)] 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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