A High-Order and Unconditionally Energy Stable Scheme for the Conservative Allen-Cahn Equation with a Nonlocal Lagrange Multiplier
- 주제(키워드) Conservative Allen-Cahn equation , Convex splitting , Mass conservation , Unconditional unique solvability , Unconditional energy stability , High-order time accuracy
- 주제(기타) Mathematics, Applied
- 설명문(일반) [Lee, Hyun Geun] Kwangwoon Univ, Dept Math, Seoul 01897, South Korea; [Shin, Jaemin] Chungbuk Natl Univ, Dept Math, Cheongju 28644, South Korea; [Lee, June-Yub] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SPRINGER/PLENUM PUBLISHERS
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000190358
- 본문언어 영어
- Published As https://doi.org/10.1007/s10915-021-01735-1
초록/요약
The conservative Allen-Cahn equation with a nonlocal Lagrange multiplier satisfies mass conservation and energy dissipation property. A challenge to numerically solving the equation is how to treat the nonlinear and nonlocal terms to preserve mass conservation and energy stability without compromising accuracy. To resolve this problem, we first apply the convex splitting idea to not only the term corresponding to the Allen-Cahn equation but also the nonlocal term. A wise implementation of the convex splitting for the nonlocal term ensures numerically exact mass conservation. And we combine the convex splitting with the specially designed implicit-explicit Runge-Kutta method. We show analytically that the scheme is uniquely solvable and unconditionally energy stable by using the fact that the scheme guarantees exact mass conservation. Numerical experiments are presented to demonstrate the accuracy and energy stability of the proposed scheme.
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