Numerical Analysis of a Continuum Model of Phase Transition

A method for solution of the Cahn-Hilliard equation is presented. Unlike previous work, the discrete equations for the new method possess a Lyapunov function. This makes it possible to prove convergence of the approximate solutions without assumptions beyond those necessary for existence and uniquen...

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Veröffentlicht in:	SIAM journal on numerical analysis 1991-10, Vol.28 (5), p.1310-1322
Hauptverfasser:	Du, Qiang, Nicolaides, R. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytical estimating Applied mathematics Approximation Boundary conditions Differential equations Error analysis Error rates Estimates Exact sciences and technology Fourier transforms Hypotheses Integers Liapunov functions Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Phase transitions Sciences and techniques of general use Uniqueness
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Beschreibung
Zusammenfassung:	A method for solution of the Cahn-Hilliard equation is presented. Unlike previous work, the discrete equations for the new method possess a Lyapunov function. This makes it possible to prove convergence of the approximate solutions without assumptions beyond those necessary for existence and uniqueness of the differential equation. Several consequences are explored.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/0728069