Discontinuous Galerkin Method for Internal Thermal Radiation Problems

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.

A space-time finite element method based on local projection stabilization in space and discontinuous Galerkin method in time for convection-diffusion-reaction equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125937 ◽

2021 ◽

Vol 397 ◽

pp. 125937

Author(s):

Ziming Dong ◽

Hong Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Diffusion Reaction ◽

Local Projection ◽

Convection Diffusion ◽

Local Projection Stabilization ◽

Reaction Equations

Coupling Runge-Kutta discontinuous Galerkin method to finite element method for compressible multi-phase flow interacting with a deformable sandwich structure

Ocean Engineering ◽

10.1016/j.oceaneng.2016.12.013 ◽

2017 ◽

Vol 130 ◽

pp. 597-610 ◽

Cited By ~ 12

Author(s):

Zeyu Jin ◽

Caiyu Yin ◽

Yong Chen ◽

Hongxing Hua

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Sandwich Structure ◽

Phase Flow ◽

Multi Phase Flow ◽

Multi Phase ◽

SIMULATION OF THE STEADY-STATE CONDUCTION-RADIATION HEAT TRANSFER PROCESS USING FINITE ELEMENT METHOD

10.20906/cps/cob-2015-1911 ◽

2015 ◽

Author(s):

RODOLFO DO LAGO SOBRAL ◽

ROGÉRIO MARTINS SALDANHA DA GAMA ◽

EDUARDO DIAS CORRÊA

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Steady State ◽

Transfer Process ◽

Radiation Heat Transfer ◽

Heat Transfer Process ◽

Radiation Heat ◽

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

China Foundry ◽

10.1007/s41230-016-5117-8 ◽

2016 ◽

Vol 13 (2) ◽

pp. 123-132 ◽

Cited By ~ 2

Author(s):

Dun-ming Liao ◽

Liu Cao ◽

Tao Chen ◽

Fei Sun ◽

Yong-zhen Jia ◽

...

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Directional Solidification ◽

Radiation Heat Transfer ◽

Solidification Process ◽

Transfer Model ◽

Radiation Heat ◽

Directional Solidification Process ◽

Superalloy Turbine Blade

Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs

Mathematics of Computation ◽

10.1090/mcom/3073 ◽

2016 ◽

Vol 85 (301) ◽

pp. 2099-2129 ◽

Cited By ~ 8

Author(s):

Alexandre Ern ◽

Friedhelm Schieweck

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Stabilized Finite Element ◽

First Order ◽

Stabilized Finite Element Method ◽

A kind of domain decomposition hierarchical time-domain finite-element method (TDFEM) discretized by discontinuous Galerkin method and solved by Crank-Nicolson algorithm

2009 Asia Pacific Microwave Conference ◽

10.1109/apmc.2009.5385412 ◽

2009 ◽

Author(s):

Z. B. Ye ◽

Chao-Fu Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Domain Decomposition ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Time Domain ◽

Element Method ◽

Crank Nicolson

Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG

Journal of Non-Newtonian Fluid Mechanics ◽

10.1016/s0377-0257(98)00176-1 ◽

1999 ◽

Vol 86 (3) ◽

pp. 281-307 ◽

Cited By ~ 84

Author(s):

J. Sun ◽

M.D. Smith ◽

R.C. Armstrong ◽

R.A. Brown

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Viscoelastic Flows ◽

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

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2015.m1412 ◽

2016 ◽

Vol 9 (1) ◽

pp. 51-86

Author(s):

Zhenhua Zhou ◽

Haijun Wu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Diffusion Problem ◽

Adaptive Finite Element Method ◽

Adaptive Finite Element ◽

Interior Penalty ◽

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.