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Morgan Pierre's Publications

Last updated October 12, 2016.


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Convergence to equilibrium for the Cahn-Hilliard equation on the unit disc (see Ref. 11)
ut=-α∆2u+ ∆ (u3-u)
α=0.05 / time step dt=0.015 / 600 iterations
random initial value
P1-P1 Finite element discretization in space
backward Euler discretization in time
Software: FreeFem++


Convergence to equilibrium for the Modified Phase Field Crystal equation (see Ref. 20)
βutt+ut=Δ[∆2u+ 2∆u+u3+(1-ε)u]
on the square (0,6π)x(0,6π) with periodic boundary conditions
β=0.1 / ε=2 / time step dt=0.25 / 200 iterations
initial value u0(x,y)=0.2+0.2cos(x)cos(y) and ut(0)=0
P1-P1-P1 Finite element discretization in space
2nd order discretization in time (scheme of Gomez and Hughes)
Software: FreeFem++