TY - JOUR
T1 - The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems
AU - Jeon , Youngmok
AU - Yi , Son-Young
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 336
EP - 359
PY - 2022
DA - 2022/03
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0154
UR - https://global-sci.org/intro/article_detail/nmtma/20355.html
KW - Parabolic interface problem, hybrid difference method, immersed interface.
AB - <p style="text-align: justify;">We propose several immersed interface hybridized difference methods
(IHDMs), combined with the Crank-Nicolson time-stepping scheme, for parabolic
interface problems. The IHDM is the same as the hybrid difference method away
from the interface cells, but the finite difference operators on the interface cells are
modified to maintain the same accuracy throughout the entire domain. For the modification process, we consider virtual extensions of two sub-solutions in the interface
cells in such a way that they satisfy certain jump equations between them. We
propose several different sets of jump equations and their resulting discrete methods
for one- and two-dimensional problems. Some numerical results are presented to
demonstrate the accuracy and robustness of the proposed methods.</p>