Constrained optimization 1 Convergence of numerical methods 1 Discontinous Galerkin methods 1 Energy 1 Energy-conservative discontinuous Galerkin method 1 Energy-conservative discontinuous galerkin method 1 Enthalpy 1 Enthalpy approach FEM approaches 1 Finite element method 1 Galerkin methods 1 Gallium 1 Linearization 1 Linearized enthalpy approach 1 Melting 1 Phase change problem 1 Problem-based 1 Second orders 1 Solid liquid phase change 1 linearized enthalpy approach 1 solid–liquid phase change 1