TY - JOUR
T1 - An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces
AU - Jiang , Kai
AU - Wang , Xin
AU - Liu , Jianggang
AU - Wei , Huayi
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 123
EP - 147
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0061
UR - https://global-sci.org/intro/article_detail/aamm/23595.html
KW - Self-consistent field theory, block copolymers, adaptive high-order surface finite element method, general curved surfaces, self-assembled patterns, $Log$ marking strategy.
AB - <p style="text-align: justify;">In this paper, we develop an adaptive high-order surface finite element
method (FEM) incorporating spectral deferred correction method for chain contour
discretization to solve polymeric self-consistent field equations on general curved surfaces. The high-order surface FEM is obtained by the high-order surface geometrical
approximation and the high-order function space approximation. Numerical results
demonstrate that the precision order of these methods is consistent with theoretical
prediction. In order to describe the sharp interface in the strongly segregated system more accurately, an adaptive FEM equipped with a new $Log$ marking strategy is
proposed. The $Log$ marking strategy can not only label the elements that need to be
refined or coarsened, but also give the refined or coarsened times, which can make
full use of the information of a posterior error estimator and improve the efficiency of
the adaptive algorithm. To demonstrate the power of our approach, we investigate the
self-assembled patterns of diblock copolymers on several distinct curved surfaces. Numerical results illustrate the efficiency of the proposed method, especially for strongly
segregated systems with economical discretization nodes.</p>