Finite element methods for the transport equation

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1. [1] CIARLET P. G. et RAVIART P. A., General Lagrange and Hermite interpolation in Rn with applications to finite element methods. Arch. Rational. Mech. Anal., 46, (1972), 177-199. Zbl0243.41004MR336957
2. [2] CIARLET P. G. et RAVIART P. A., Interpolation theory over curved elements with applications to finite element methods. Computer Methods in Applied Mechanics and Engineering 1 (1972), 217-249. Zbl0261.65079MR375801
3. [3] CIARLET P. G. et RAVIART P. A., The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical Foundations of the Finite Element Method with Applicationsto Partial Differential Equations. (A. K. Aziz, ed.) 409-474, Academic Press, New York, 1972. Zbl0262.65070MR421108
4. [4] DUPONT T., Galerkin methods for first order hyperbolics: an example. Siam J. Numer. Anal. Vol. 10, n° 5 (1973). Zbl0237.65070MR349046
5. [5] FRIEDRICHS K. O., Symmetric positive differential equations. Comm. on pure and appl. math. II (1958), 333-418. Zbl0083.31802MR100718
6. [6] KAPER H. G., LEAF G. K. and LINDEMAN A. J., Application of finite element techniques for the numerical solution of the neutron transport and diffusion equations, Proceedings of Second Conference on Transport Theory, USAEC DTIE CONF-710302 (1971), 258-285. 
7. [7] LATHROP K. D., Spatial differencing of the Transport equation : Positivity VS. Accuracy. Journ. of Comp. Physics 4 (1969), 475-498. Zbl0199.50703
8. [8] LATHROP K. D., Transport theory numerical methods. Submitted to American Nuclear Society Topical Meeting on Mathematical Models and Computational Techniques for Analysis of Nuclear Systems (1973) LA-UR-73-517, Los Alamos Scientific Laboratory (1973). 
9. [9] LATHROP K. D. and CARLSON B. G., Numerical Solution of the Boltzmann Transport Equation. Journ. of Comp. Physics 2 (1967), 173-197. Zbl0171.13902MR241013
10. [10] LATHROP K. D. and CARLSON B. G., Transport Theory. The method of Discrete Ordinates. Computing Methods in Reactor Physics (Greenspan, H., C. N. Kelerband D. Okrent, editors), 165-266, Gordon and Breach, 1968. 
11. [11] LESAINT P., Finite element methods for symmetric hyperbolic equations. Numer. Math. 21(1973), 244-255. Zbl0283.65061MR341902
12. [12] LESAINT P. et GERIN-ROZE J., Isoparametric finite element methods for the neutron transport equation.To appear in Int. Jl. Num. Meth. Eng. Zbl0331.65084
13. [13] LESAINT P. et RAVIART P. A., On a finite element method for solving the neutron transport equation.To appear. Zbl0341.65076
14. [14] MILLER W. F. Jr., LEWIS E. E. and Rossow E. C., The application of phase-pace finite elements to the two dimensional transport equation in x - y geometry. Nucl. Sci.and Eng. 52, 12 (1973). 
15. [15] ONISHI T., Application of finite element solution technique to neutron diffusion and transport equations. Proceedings of Conf. on new developments in Reactor Mathematics and Applications, USAEC DTIE CONF-710107, 258 (1971). 
16. [16] PHILIPPS R. S. and LEONARD SARASON, Singular symmetric positive first order differential operators. Journal of Mathematics and Mechanics 15 (1966), 235-271. Zbl0141.28701MR186902
17. [17] REED W. H. and HILL T. R., Triangular mesh methods for the neutron transport equation. Submitted to American Nuclear Society Topical Meeting on Mathematical Models and Computational Techniques for Analysis of Nuclear Systems (1973). LA UR-73-479, Los Alamos Laboratory, 1973. 
18. [18] STRANG G. and Fix G., An analysis of finite element method, Prentice Hall, New York, 1973. Zbl0356.65096MR443377
19. [19] ZIENKIEWICZ O. C, The Finite Element Method in Engineering Science. MacGraw-Hill, London, 1971. Zbl0237.73071MR315970
20. [20] GIRAULT V., Theory of a finite difference method on irregular networks. Siam J. Numer. Anal., vol. 11, N. 2, March 1974. Zbl0296.65049MR431730

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