TY - JOUR
T1 - An Optimal-Order Error Estimate for a Finite Difference Method to Transient Degenerate Advection-Diffusion Equations
AU - T. Lu & J. Jia
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 56
EP - 72
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/611.html
KW - Convergence analysis, degenerate advection-diffusion equations, finite difference methods, optimal-order error estimates.
AB - <p style="text-align: justify;">We prove an optimal-order error estimate in a degenerate-diffusion
weighted energy norm for implicit Euler and Crank-Nicolson finite difference
methods to two-dimensional time-dependent advection-diffusion equations with
degenerate diffusion. In the estimate, the generic constants depend only on
certain Sobolev norms of the true solution but not on the lower bound of the
diffusion. This estimate, combined with a known stability estimate of the true
solution of the governing partial differential equations, yields an optimal-order
estimate of the finite difference methods, in which the generic constants depend
only on the Sobolev norms of the initial and right-hand side data.</p>