Figure 3.

Plot of convergence in L¹ and L^∞ error norm of the velocity u, liquid temperature T⁺, solid temperature T⁻, solute concentration C and interface melting speed v as a function of ε. Each norm is calculated within the appropriate domain of the reference variable. Clear $\mathcal{O}({\epsilon }^2)$ convergence is observed in L¹ norm using optimal parameters. $\mathcal{O}(\epsilon )$ convergence in L^∞ norm occurs for the temperature because of the non-differentiability of the reference solution. (Online version in colour.)