TY - JOUR
T1 - A priori error analysis for transient problems using Enhanced Velocity approach in the discrete-time setting
AU - Amanbek, Yerlan
AU - Wheeler, Mary F.
N1 - Funding Information:
First author thanks Drs. T. Arbogast and I. Yotov for some helpful discussions during analysis of method. First author would like to acknowledge support of the Faculty development Competitive Research Grant (Grant No. 110119FD4502 ), Nazarbayev University (Kazakhstan).
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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. These error estimates are useful in the determining of time step size and the space discretization size.
AB - 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. These error estimates are useful in the determining of time step size and the space discretization size.
KW - A priori error analysis
KW - Darcy flow
KW - Enhanced velocity
KW - Error estimates
KW - Mixed finite element method
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U2 - 10.1016/j.cam.2019.05.009
DO - 10.1016/j.cam.2019.05.009
M3 - Article
AN - SCOPUS:85066104045
SN - 0377-0427
VL - 361
SP - 459
EP - 471
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -