TY - JOUR
T1 - A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms
AU - Ngondiep , Eric
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1005
EP - 1026
PY - 2021
DA - 2021/06
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2020-0206
UR - https://global-sci.org/intro/article_detail/aamm/19252.html
KW - Two-dimensional advection-diffusion equation, time dependent dispersion coefficients, Crank-Nicolson approach, a two-level factored Crank-Nicolson method, stability and convergence rate.
AB - <p style="text-align: justify;">This paper deals with a two-level factored Crank-Nicolson method in an approximate solution of two-dimensional evolutionary advection-diffusion equation with time dependent dispersion coefficients and sink/source terms subjects to appropriate initial and boundary conditions. The procedure consists of reducing problems in many space variables into a sequence of one-dimensional subproblems and then find the solution of tridiagonal linear systems of equations. This considerably reduces the computational cost of the algorithm. Furthermore, the proposed approach is fast and efficient: unconditionally stable, temporal second order accurate and fourth order convergent in space and it improves a large class of numerical schemes widely studied in the literature for the considered problem. The stability of the new method is deeply analyzed using the $L^{\infty}(t_{0},T_{f};L^{2})$-norm whereas the convergence rate of the scheme is numerically obtained in the $L^{2}$-norm. A broad range of numerical experiments are presented and critically discussed.</p>