TY - JOUR
T1 - A Time Second-Order Characteristic Finite Element Method for Nonlinear Advection-Diffusion Equations
AU - Hou , Baohui
AU - Liang , Dong
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 276
EP - 296
PY - 2018
DA - 2018/10
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12804.html
KW - Nonlinear advection-diffusion equations, characteristic method, characteristic average, characteristic extrapolation, time second-order, error estimate, population dynamics.
AB - <p style="text-align: justify;">In this paper, a new time second-order characteristic finite element method is proposed
and analyzed for solving the advection-diffusion equations involving a nonlinear right side term. In
order to obtain a time second-order characteristic scheme, the global derivative term transferred
from the time derivative and advection terms is discretized by using difference operator along the
characteristics, the diffusion term is discretized by the average operator along the characteristics,
while specially a second-order extrapolation along the characteristics is applied to the right side
nonlinear function. We analyze and prove that the proposed scheme for the nonlinear advection-diffusion
equations has second order accuracy in time step size, which improves the first order
accuracy in time of the classical characteristic methods. The proposed characteristic FEM scheme
allows to use large time step sizes in computation. Numerical tests are taken to show the accuracy
of our proposed scheme, and the case of single-species population dynamics is further simulated
and analyzed by using our method and numerical results show its advantage and effectiveness.</p>