Open Access
Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
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Page(s) | 2949 - 2980 | |
DOI | https://doi.org/10.1051/m2an/2021077 | |
Published online | 06 December 2021 |
- R.E. Aamodt and K.M. Case, Useful identities for half-space problems in linear transport theory. Ann. Phys. 21 (1963) 284–301. [CrossRef] [Google Scholar]
- M. Abramovitz and I. Stegun, Handbook of Mathematical Functions. National Bureau of Standards, Washington, DC (1972). [Google Scholar]
- R. Bianchini and L. Gosse, A truly two-dimensional discretization of drift-diffusion equations on Cartesian grids. SIAM J. Numer. Anal. 56 (2018) 2845–2870. [CrossRef] [MathSciNet] [Google Scholar]
- R. Bianchini, L. Gosse and E. Zuazua, A two-dimensional “`FLEA on the elephant’” phenomenon and its numerical visualization. SIAM Mult. Model. Simul. 17 (2019) 137–166. [CrossRef] [Google Scholar]
- G. Birkhoff and I. Abu-Shumays, Harmonic solutions of transport equations. J. Math. Anal. App. 28 (1969) 211–221. [CrossRef] [Google Scholar]
- G. Birkhoff and I. Abu-Shumays, Exact analytic solutions of transport equations, J. Math. Anal. App. 32 (1970) 468–481. [CrossRef] [Google Scholar]
- G. Bretti and L. Gosse, Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis. SN Part. Differ. Equ. App. 2 (2021) 695. [Google Scholar]
- G. Bretti, L. Gosse and N. Vauchelet, L-splines as diffusive limits of dissipative kinetic models. Vietnam J. Math. 49 (2021) 651–671. [CrossRef] [MathSciNet] [Google Scholar]
- M. Briani, R. Natalini and G. Russo, Implicit–explicit numerical schemes for jump-diffusion processes. Calcolo 44 (2007) 33–57. [CrossRef] [MathSciNet] [Google Scholar]
- C. Buet, B. Despres and G. Morel, Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport. Adv. Comput. Math. 46 (2020) 1–27. [CrossRef] [Google Scholar]
- K.M. Case, Elementary solutions of the transport equation and their applications. Ann. Phys. 9 (1960) 1–23. [CrossRef] [Google Scholar]
- K.M. Case and P.F. Zweifel, Linear Transport Theory. Addison-Wesley Series in Nuclear Engineering. Addison-Wesley Publishing Company (1967). [Google Scholar]
- J.G. Conlon, Fundamental solutions for the anisotropic neutron transport equation. Proc. R. Soc. Edinburgh 82A (1978) 325–350. [CrossRef] [Google Scholar]
- B. Despres and C. Buet, The structure of well-balanced schemes for Friedrichs systems with linear relaxation. Appl. Math. Comput. 272 (2016) 440–459. [MathSciNet] [Google Scholar]
- R. Estrada, On Pizzetti’s formula. Asymptotic Anal. 111 (2019) 1–14. [MathSciNet] [Google Scholar]
- L. Flatto, Functions with a mean value property. J. Math. Mech. 10 (1961) 11–18. [MathSciNet] [Google Scholar]
- L. Gosse, Computing Qualitatively Correct Approximations of Balance Laws: Exponential-fit, Well-balanced and Asymptotic-Preserving. Vol. 2 of SIMAI Springer Series. Springer-Verlag Italia (2013). [CrossRef] [Google Scholar]
- L. Gosse, A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation. BIT Numer. Math. 55 (2015) 433–458. [CrossRef] [Google Scholar]
- L. Gosse, A well-balanced scheme able to cope with hydrodynamic limits for linear kinetic models. Appl. Math. Lett. 42 (2015) 15–21. [CrossRef] [MathSciNet] [Google Scholar]
- L. Gosse, Viscous equations treated with L-splines and Steklov-Poincaré operator in two dimensions. In: Innovative Algorithms and Analysis. Springer, Cham (2017). [CrossRef] [Google Scholar]
- L. Gosse, L-splines and viscosity limits for well-balanced schemes acting on linear parabolic equations. Acta App. Math. 153 (2018) 101–124. [CrossRef] [Google Scholar]
- L. Gosse and G. Toscani, An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations. C.R. Math. Acad. Sci. Paris 334 (2002) 337–342. [CrossRef] [MathSciNet] [Google Scholar]
- L. Gosse and N. Vauchelet, Numerical high-field limits in two-stream kinetic models and 1D aggregation equations. SIAM J. Sci. Comput. 38 (2016) A412–A434. [CrossRef] [Google Scholar]
- L. Gosse and N. Vauchelet, Some examples of kinetic schemes whose diffusion limit is Il’in’s exponential-fitting. Numer. Math. 141 (2019) 627–680. [CrossRef] [MathSciNet] [Google Scholar]
- L. Gosse and N. Vauchelet, A truly two-dimensional, asymptotic-preserving scheme for a discrete model of radiative transfer. SIAM J. Numer. Anal. 58 (2020) 1092–1116. [CrossRef] [MathSciNet] [Google Scholar]
- H. Han and Z. Huang, The tailored finite point method. Comput. Methods Appl. Math. 14 (2014) 321–345. [CrossRef] [MathSciNet] [Google Scholar]
- H. Han, Z. Huang and R.B. Kellogg, A tailored finite point method for a singular perturbation problem on an unbounded domain. J. Sci. Comput. 36 (2008) 243–261. [CrossRef] [MathSciNet] [Google Scholar]
- P.-L. Lions and G. Toscani, Diffusive limit for finite velocity Boltzmann kinetic models. Riv. Math. Iberoamericana 13 (1997) 473–513. [CrossRef] [Google Scholar]
- Y.A. Melnikov and M.Y. Melnikov, Green’s Functions: Construction and Applications. Vol. 42 of De Gruyter Studies in Mathematics. De Gruyter, Berlin, Boston (2012). [Google Scholar]
- S. Michalik, Summable solutions of some partial differential equations and generalised integral means. J. Math. Anal. Appl. 444 (2016) 1242–1259. [CrossRef] [MathSciNet] [Google Scholar]
- C.W. Misner, Spherical harmonic decomposition on a cubic grid. Class. Quantum Grav. 21 (2004) S243. [CrossRef] [Google Scholar]
- L. Pareschi and G. Russo, Implicit–explicit Runge-Kutta schemes and applications to hyperbolic system with relaxation. J. Sci. Comput. 25 (2005) 129–155. [MathSciNet] [Google Scholar]
- X. Yang, F. Golse, Z. Huang and S. Jin, Numerical study of a domain decomposition method for a two-scale linear transport equation. Networks Heter. Media 1 (2006) 143–166. [CrossRef] [Google Scholar]
- L. Zalcman, Mean values and differential equations. Israel J. Math. 14 (1973) 339–352. [CrossRef] [MathSciNet] [Google Scholar]
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