Table A1. Error in the phase-field... | Emerald Publishing

Table A1.

Error in the phase-field approximation for varying $ρ_{i}^{\infty}$ at time $u_{0} t_{n} / ε = 48$

User-controlled parameters	$\| \| φ_{n} - φ_{ref} (t_{n}, \cdot) \| \|_{L^{2} (Ω)}$ $u_{0} τ / ε = 1 / 4$	$\| \| φ_{n} - φ_{ref} (t_{n}, \cdot) \| \|_{L^{2} (Ω)}$ $u_{0} τ / ε = 1$
$ρ_{i}^{\infty} = 0$	$3.64 \cdot 10^{- 6}$	$2.82 \cdot 10^{- 4}$
$ρ_{i}^{\infty} = 0.2$	$1.85 \cdot 10^{- 7}$	$1.33 \cdot 10^{- 4}$
$ρ_{i}^{\infty} = 0.4$	$9.65 \cdot 10^{- 7}$	$1.57 \cdot 10^{- 5}$
$ρ_{i}^{\infty} = 0.5$	$7.08 \cdot 10^{- 7}$	$7.10 \cdot 10^{- 5}$
$ρ_{i}^{\infty} = 0.6$	$5.25 \cdot 10^{- 7}$	$1.01 \cdot 10^{- 4}$
$ρ_{i}^{\infty} = 0.8$	$2.97 \cdot 10^{- 7}$	$1.04 \cdot 10^{- 4}$
$ρ_{i}^{\infty} = 1$	$3.91 \cdot 10^{- 6}$	Unstable
$ρ_{1}^{\infty} = 0.6 ρ_{2}^{\infty} = 0.8$	$4.53 \cdot 10^{- 7}$	$7.38 \cdot 10^{- 5}$