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Article Contents

# A rapidly converging phase field model

• We propose a phase field model that approximates its limiting sharp interface model (free boundary problem) up to second order in interface thickness. A broad range of double-well potentials can be utilized so long as the dynamical coefficient in the phase equation is adjusted appropriately. This model thereby assures that computation with particular value of interface thickness $\varepsilon$, will differ at most by $O(\varepsilon^2$) from the limiting sharp interface problem. As an illustration, the speed of a traveling wave of the phase field model is asymptotically expanded to demonstrate that it differs from the speed of the traveling wave of the limit problem by $O(\varepsilon^2)$.
Mathematics Subject Classification: Primary: 80A22, 80M35; Secondary: 35K55.

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