On a Finite Element Method for Solving the Neutron Transport Equation

 Access to full text

 Full (PDF)

1. [1] Axelsson, O., "A class of A-stable methods", B.I.T.9 (1969), 185-199. Zbl0208.41504MR255059
2. [2] de Boor, C., and B. Swartz "Collocation at Gaussian points", SIAM J. Numer. Anal.10. (1973) 582-606. Zbl0232.65065MR373328
3. [3] Butcher, J.C., "Implicit Runge-Kutta processes" Math. Comp.18 (1964), 50-64. Zbl0123.11701MR159424
4. [4] Ciarlet, P.G., and P.A. Raviart "General Lagrange and Hermite interpolation in ${ℝ}^n$ with applications to finite element methods", Arch. Rat. Mech. Anal.46.(1972), 177-199. Zbl0243.41004MR336957
5. [5] Ciarlet, P.G., and P.A. Raviart "Interpolation theory over curved elements, with applications to finite element methods", Comp. Meth. Appl. Mech. Eng.1 (1972), 217-249. Zbl0261.65079MR375801
6. [6] Ciarlet, P.G., and P.A. Raviart "The combined effect of curved boundaries and numerical integration in isoparametric finite element methods", The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A.K. Aziz, Editor), 409-474, Academic Press, New-York, 1972. Zbl0262.65070MR421108
7. [7] Crcuzeix, M., Thesis, to appear. Zbl05.0337.02
8. [8] Friedrichs, K.O., "Symmetric positive differential equations", Comm. Pure Appl. Math.11 (1958), 333-418 Zbl0083.31802MR100718
9. [9] Hulme, B.L., "Discrete Galerkin and related one-step methods differential equations", Math. Comp.26 (1972), 881-891. Zbl0272.65056MR315899
10. [10] Kaper, H.G., G.K. Leaf and A.J. Lindeman "Application of finite element techniques for the numerical solution of the neutron transport and diffusion equations" Proc. Conf. on Transport Theory, 2nd Conf. 710107, Los Alamos (1971). 
11. [11] Lesaint, P., "Finite element methods for symmetric hyperbolic equations", Numer. Math21 (1973), 244-255. Zbl0283.65061MR341902
12. [12] Lesaint, P. , "Finite element methods for the transport equation", to appear in RAIRO, série Mathématiques. Zbl0313.65103MR913315
13. [13] Lesaint, P. , Thesis, to appear. 
14. [14] Lesaint, P., and J. Gérin-Roze "Isoparametric finite element methods for the neutron transport equation", to appear. Zbl0331.65084
15. [15] Miller, W.F. Jr, E.E Lewis, and E.C. Rossow "The application of phase-space finite elements to the two-dimensional transport equation in x-y geometry", to appear in Nucl. Sci. Eng. 
16. [16] Ohnishi, T., "Application of finite element solution technique to neutron diffusion and transport equations", Proc conf. on New Developments in Reactor Mathematics and Applications, CONF-710302, Idaho Falls (1971). 
17. [17] Reed, W.H., and T.R. Hill "Triangular mesh methods for the neutron transport equation" to appear in Proc. Amer. Nucl. Soc.