scholarly journals Stability and convergence of a finite element method for solving the Stefan problem

1976 ◽  
Vol 12 (2) ◽  
pp. 539-563 ◽  
Author(s):  
Masatake Mori
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stefan Problem ◽  
Stability And Convergence ◽  
Element Method

scholarly journals Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation

2018 ◽  
Vol 16 (1) ◽  
pp. 1091-1103 ◽  
Author(s):  
Leilei Wei ◽  
Yundong Mu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discontinuous Galerkin ◽  
Local Discontinuous Galerkin Method ◽  
Stability And Convergence ◽  
Lax Equation ◽  
Local Discontinuous Galerkin ◽  
Discontinuous Galerkin Finite Element ◽  
Numerical Performance ◽  
Element Method

AbstractIn this paper we develop and analyze the local discontinuous Galerkin (LDG) finite element method for solving the general Lax equation. The local discontinuous Galerkin method has the flexibility for arbitrary h and p adaptivity, and allows for hanging nodes. By choosing the numerical fluxes carefully we prove stability and give an error estimate. Finally some numerical examples are computed to show the convergence order and excellent numerical performance of proposed method.

scholarly journals An enthalpy-based finite element method for solving two-phase Stefan problem

2019 ◽  
Vol 4 (1) ◽  
pp. 43
Author(s):  
Dede Tarwidi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Godunov Method ◽  
Two Phase ◽  
Interface Position ◽  
Enthalpy Formulation ◽  
Element Method

Stefan problem is a problem involving phase transition from solid to liquid or vice versa where boundary between solid and liquid regions moves as function of time. This paper presents numerical solution of one-dimensional two-phase Stefan problem by using finite element method. The governing equations involved in Stefan problem consist of heat conduction equation for solid and liquid regions, and also transition equation in interface position (moving boundary). The equations are difficult to solve by ordinary numerical method because of the presence of moving boundary. As consequence, the equations is reformulated into the form of internal energy (enthalpy). By the enthalpy formulation, solution of the heat conduction equations is no longer concerning the phase state of material. The advantage of the enthalpy formulation is that, finite element method can be easily implemented to solve Stefan problem. Numerical simulation of interface position, temperature profile, and temperature history has good agreement with the exact solution. The approximation of interface position using finite element method was found that it is more accurate than the approximation by using Godunov method. The simulation results also reveal that the finite element method for solving Stefan problem have smaller mean absolute error than the Godunov method.

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