Discontinous Galerkin methods Finite element method 3 Galerkin methods 3 Approximate solution 1 Constrained optimization 1 Convergence of numerical methods 1 Diffusion 1 Discontinuous Galerkin 1 Discontinuous Galerkin finite element methods 1 Discontinuous Galerkin finite-element method 1 Discontinuous galerkin 1 Embedded 1 Energy 1 Energy-conservative discontinuous Galerkin method 1 Energy-conservative discontinuous galerkin method 1 Enthalpy 1 Enthalpy approach 1 Error estimates 1 Errors 1 FEM approaches 1 Gallium 1 Hp-FEM 1 Hybridized 1 Hybridized discontinuous galerkin 1 Interior penalties 1 Linearization 1 Linearized enthalpy approach 1 Local variations 1 Melting 1 Mesh generation 1