4.6 Article

Maximum Principle Preserving Schemes for Binary Systems with Long-Range Interactions

期刊

JOURNAL OF SCIENTIFIC COMPUTING
卷 84, 期 2, 页码 -

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SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-020-01286-x

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Ohta-Kawasaki model; Gradient flow; Maximum principle preservation; Energy stability

资金

  1. Simons Foundation [357963]

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We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear termf(phi) in the Ohta-Kawasaki free energy functional, we show that the Allen-Cahn-Ohta-Kawasaki dynamics is maximum principle preserving. We further design some first order energy stable numerical schemes which inherit the maximum principle preservation in both semi-discrete and fully-discrete levels. Furthermore, we apply the maximum principle preserving schemes to a general framework for binary systems with long-range interactions. We also present some numerical results to support our theoretical findings.

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