Coupling of finite element method and discontinuous Galerkin method to simulate viscoelastic flows

2017 ◽  
Vol 86 (6) ◽  
pp. 414-432 ◽  
Author(s):  
Puyang Gao ◽  
Jie Ouyang ◽  
Wen Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Viscoelastic Flows ◽  
Element Method

Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method

2016 ◽  
Vol 9 (1) ◽  
pp. 51-86
Author(s):  
Zhenhua Zhou ◽  
Haijun Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Diffusion Problem ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Interior Penalty ◽  
Element Method

AbstractAn adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works are done to overcome the difficulties caused by the additional penalty terms.

Discontinuous Galerkin Method for Internal Thermal Radiation Problems

2003 ◽  
Author(s):  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Integral Differential Equation

The internal thermal radiation phenomena are described by a first-order integral-differential equation, which poses an intrinsic problem for the popular diffusion-based Galerkin finite element method. By allowing for discontinuity across the internal inter-element boundaries, the finite element procedure can be adapted to solve the integral-differential equation. This paper discusses a numerical procedure based on the discontinuous Galerkin method for the solution of radiation heat transfer involving participating media. Detailed formulation using the discontinuous Galerkin method for internal radiation heat transfer calculations is given. The coupling of the method with the conventional finite element method for mixed heat transfer calculations is also presented.

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