FINITE ELEMENT APPROXIMATION OF NONLOCAL HEAT RADIATION PROBLEMS
1998 ◽
Vol 08
(06)
◽
pp. 1071-1089
◽
Keyword(s):
This paper focuses on finite element error analysis for problems involving both conductive and radiative heat transfers. The radiative heat exchange is modeled with a nonlinear and nonlocal term that also makes the problem non-monotone. The continuous problem has a maximum principle which suggests the use of inverse monotone discretizations. We also estimate the error due to the approximation of the boundary by showing continuous dependence on the geometric data for the continuous problem. The final result of this paper is a rigorous justification and error analysis for methods that use the so-called view factors for numerical modeling of the heat radiation.
2018 ◽
Vol 78
(3)
◽
pp. 1862-1892
◽
2021 ◽
Vol 381
◽
pp. 113008
2008 ◽
pp. 637-644
◽
2005 ◽
Vol 180
(1)
◽
pp. 181-190
◽
Keyword(s):
1996 ◽
Vol 30
(6)
◽
pp. 743-762
◽
2004 ◽
Vol 38
(3)
◽
pp. 563-578
◽
2012 ◽
Vol 11
(1)
◽
pp. 339-364
◽
2014 ◽
Vol 52
(1)
◽
pp. 97-119
◽
2014 ◽
Vol 14
(4)
◽
pp. 419-427
◽