Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 234-254 |
| Number of pages | 21 |
| Journal | East Asian Journal on Applied Mathematics |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2021 Feb |
Bibliographical note
Funding Information:One of us (J.Y.) is supported by the China Scholarship Council (201908260060) and the other (J.S.K.) by the Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A2C1003053).
Publisher Copyright:
c 2021 Global-Science Press
Keywords
- Finite difference method
- Ohta-Kawasaki model
- Second-order accuracy
- Unconditional energy stability
ASJC Scopus subject areas
- Applied Mathematics