A constrained convex splitting scheme for the vector-valued Cahn-Hilliard equation
- 주제(기타) 수치해석
- 설명문(URI) https://www.kci.go.kr/kciportal/ci/sereArticleSearch/ciSereArtiView.kci?sereArticleSearchBean.artiId=ART002447173
- 관리정보기술 faculty
- 등재 KCI등재
- 발행기관 한국산업응용수학회
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160831
- 본문언어 영어
초록/요약
In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn–Hilliard (vCH) equation.In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.
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