@Article{EAJAM-11-2,
author = {Yang, Junxiang and Kim, Junseok},
title = {An Energy Stable Second-Order Accurate Scheme for Microphase Separation of Periodic Diblock Copolymers},
journal = {East Asian Journal on Applied Mathematics},
year = {2021},
volume = {11},
number = {2},
pages = {234--254},
abstract = {<p style="text-align: justify;">A linear, unconditionally energy stable, and second-order accurate numerical
scheme for the Ohta-Kawasaki equation modeling the diblock copolymer dynamics is
proposed. The temporal discretisation is based on the Crank-Nicolson temporal discretisation and extrapolation. To suppress the dominance of nonlinear term, a proper stabilising parameter is used. All nonlinear parts are linearised by using the extrapolation from
the information at preceding time levels. To solve the resulting linear system, an efficient
linear multigrid algorithm is used. The unconditionally energy stability, mass conservation, and unique solvability of the scheme are analytically proved. In two-dimensional
case, we run convergence and stability tests, and consider pattern formations for various
average concentrations. Pattern formations in three-dimensional space are also studied.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.240620.071020},
url = {https://global-sci.com/article/82501/an-energy-stable-second-order-accurate-scheme-for-microphase-separation-of-periodic-diblock-copolymers}
}