Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections

2012 ◽  
Vol 93 (3) ◽  
pp. 302-328 ◽  
Author(s):  
Santiago Badia ◽  
Ramon Planas ◽  
Juan Vicente Gutiérrez-Santacreu
Keyword(s):  
Finite Element ◽  
Operator Splitting ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Unconditionally Stable ◽  
Splitting Algorithms ◽  
Stabilized Finite Element ◽  
Incompressible Magnetohydrodynamics ◽  
Magnetohydrodynamics System

A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
L. Zhang ◽  
J. M. Zhao ◽  
L. H. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Element Method

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.

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