Error analysis for the finite element approximation of a radiative transfer model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 30 (1996) no. 6, p. 743-762
@article{M2AN_1996__30_6_743_0,
author = {F\"uhrer, Christian and Rannacher, Rolf},
title = {Error analysis for the finite element approximation of a radiative transfer model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {30},
number = {6},
year = {1996},
pages = {743-762},
zbl = {0866.65093},
mrnumber = {1419937},
language = {en},
url = {http://www.numdam.org/item/M2AN_1996__30_6_743_0}
}

Führer, Christian; Rannacher, Rolf. Error analysis for the finite element approximation of a radiative transfer model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 30 (1996) no. 6, pp. 743-762. http://www.numdam.org/item/M2AN_1996__30_6_743_0/

[1] M. Asadzadeh, 1986, Convergence Analysis of Some Numencal Methods for Neutron Transport and Vlasov Equations, Ph. D. thesis, Chalmers University of Technology, Göteborg, Sweden.

[2] L. H. Auer, 1984, Difference equations and linearization methods for radiative transfer methods in radiative transfer, Methods in Radiative Transfer, W. Kalk-ofen ed., Cambridge.

[3] C. Carstensen, E. Stephan, A posteriori Estimates tor Boundary Element Methods, to appear in Math. Comp. | MR 1320892 | Zbl 0831.65120

[4] K. Eriksson, C. Johnson, 1988, An adaptive finite element method tor linear elliptic problems, Math. Comp., 50, pp. 361-383. | MR 929542 | Zbl 0644.65080

[5] K. Eriksson, C. Johnson, 1991, Adaptive finite element methods for parabolic problems I : A linear model problem, SIAM. J. Num. Anal., 28, pp. 43-77. | MR 1083324 | Zbl 0732.65093

[6] C. Fuhrer, 1993, Finite-Elemente-Diskretisterungen zur Lösung der 2D-Strahlungstransportgleiehung, Diploma thesis, Heidelberg University.

[7] C. Fuhrer, 1993, A comparative study on finite element solvers for hyperbolic problems with applications to radiative transfer, Preprint 93-65, SFB 359, Heidelberg University.

[8] C. Fuhrer, G. Kanschat, 1994, Error control in radiative transfer, Preprint, Heidelberg University, 6/94 to appear in Computing. | MR 1461969

[9] I. Graham, 1982, Galerkin methods for second kind integral equations with singularities, Math. Comp., 39, pp. 519-533. | MR 669644 | Zbl 0496.65068

[10] W. Hackbusch, 1989, Integralgleichungen - Theorie und Numerik, Teubner, Stuttgart. | MR 1010893 | Zbl 0681.65099

[11] C. Johnson, J. Pitkaranta, 1983, Convergence of a fuily discrete scheme for two-dimensional neutron transport, SIAM J. Num. Anal., 20, pp. 951-966. | MR 714690 | Zbl 0538.65097

[12] S. G. Mlkhlin, 1965, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, Oxford. | MR 185399 | Zbl 0129.07701

[13] P. Nelson, H. P. Victory 1980, Convergence of two-dimensional Nyström discrete ordinales in solving the linear transport equation, Num. Anal., 34, pp. 353-370. | MR 577403 | Zbl 0414.65074

[14] J. Nltsche, A. Schatz, 1974, Interior estimates for Ritz-Galerkin methods, Math. Comp., 28, pp. 937-958. | MR 373325 | Zbl 0298.65071

[15] Papkalla R., 1993, Linienentstehung in Akkretionsscheiben, Ph. D. thesis, Heidelberg University.

[16] J. Pltkaränta, 1979, On the differential properties of solutions to Fredholm equations with weakly singular kernels, J. Inst. Math. Appl., 24, pp. 109-119. | MR 544428 | Zbl 0423.45004

[17] I. Sloan, V. Thomée, 1985, Superconvergence of the Galerkin iterates forintegral equations of the second kind, J. Int. Eqs., 9, pp. 1-230. | MR 793101 | Zbl 0575.65131

[18] S. Turek, 1995 A generalized mean intensity approach for the numerical solution of the radiative transfer equation, Computing, 54, Nr. 1, 27-38. | MR 1314954 | Zbl 0822.65129

[19] W. L. Wendland, Yu De-Hao, 1992 A posteriori local error estimates of boundary element methods with some pseudo differential equations on closed curves, J. Comp. Math. 10, Nr. 3, pp. 273-289. | MR 1167929 | Zbl 0758.65072