Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System

John W. Barrett, James F. Blowey
2002 SIAM Journal on Numerical Analysis  
We consider a fully practical nite element approximation of an Allen-Cahn/Cahn-Hilliard system with a degenerate mobility and a logarithmic free energy. This system arises in the modelling of phase separation and ordering in binary alloys. In addition to showing well-posedness and stability bounds for our approximation, w e p r o ve convergence in one space dimension. Finally some numerical experiments are presented. Key words. degenerate second/fourth order parabolic equations, degenerate
more » ... ns, degenerate parabolic system, Allen-Cahn/Cahn-Hilliard, order-disorder, phase separation, nite elements, convergence analysis. AMS subject classi cations. 35B65, 35G25, 35K50, 35K55, 35K65, 65M12, 65M60, 82C26. 4 ; s 2 : (1.3b)
doi:10.1137/s0036142900382144 fatcat:nn5oep335ndf7pz736z2shemam