Arturo Hidalgo, Michael Dumbser, Eleuterio F. Toro
. Preface to the Focused Issue on High-Order Numerical Methods for Evolutionary PDEs[J]. Communications on Applied Mathematics and Computation, 2023
, 5(2)
: 529
-531
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DOI: 10.1007/s42967-022-00229-7
1. Abgrall, R., Maria, H.V.:Neural network-based limiter with transfer learning. Commun. Appl. Math. Comput. (2020). https://doi.org/10.1007/s42967-020-00087-1
2. Abgrall, R., Nordström, J., Öffner, P., Tokareva, S.:Analysis of the SBP-SAT stabilization for finite element methods part II:entropy stability. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-020-00086-2
3. Barsukow, W.:Stationarity preservation properties of the active flux scheme on Cartesian grids. Commun. Appl. Math. Comput. (2020). https://doi.org/10.1007/s42967-020-00094-2
4. Bergami, M., Boscheri, W., Dimarco, G.:A high-order conservative semi-Lagrangian solver for 3D free surface flows with sediment transport on Voronoi meshes. Commun. Appl. Math. Comput. (2020). https://doi.org/10.1007/s42967-020-00093-3
5. Drouillet, A., Le Tellier, R., Loubère, R., Peybernes, M., Viot, L.:Multi-dimensional simulation of phase change by a 0D-2D model coupling via Stefan condition. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00157-y
6. Dumbser, M., Balsara, D.S., Toro, E.F., Munz, C.-D.:A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. J. Comput. Phys. 227(18), 8209-8253 (2008)
7. Dumbser, M., Enaux, C., Toro, E.F.:Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J. Comput. Phys. 227(8), 3971-4001 (2008)
8. Dumbser, M., Schwartzkopff, T., Munz, C.-D.:Arbitrary high order finite volume schemes for linear wave propagation. In:Book Series Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 91, pp. 1612-2909. Springer, Berlin (2006)
9. González-Aguirre, J. C., González-Vázquez, J. A., Alavez-Ramírez, J., Silva, R., Vázquez-Cendón, M. E.:Numerical simulation of bed load and suspended load sediment transport using wellbalanced numerical schemes. Commun. Appl. Math. Comput. (2022). https://doi.org/10.1007/s42967-021-00162-1
10. Guermond, J.-L., Popov, B., Saavedra, L.:Second-order invariant domain preserving ALE approximation of Euler equations. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00165-y
11. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.R.:Uniformly high order accuracy essentially non-oscillatory schemes III. J. Comput. Phys. 71, 231-303 (1987)
12. Jiang, G.S., Shu, C.-W.:Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202-228 (1996)
13. Luna, P., Hidalgo, A.:Numerical approach of a coupled pressure-saturation model describing oil-water flow in porous media. Commun. Appl. Math. Comput. (2022). https://doi. org/10. 1007/ s42967-022-00200-6
14. Machado, G.J., Clain, S., Loubère, R.:A posteriori stabilized sixth-order finite volume scheme with adaptive stencil construction:basics for the 1D steady-state hyperbolic equations. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00140-7
15. Markert, J., Gassner, G., Walch, S.:A sub-element adaptive shock capturing approach for discontinuous Galerkin methods. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00120-x
16. Sjögreen, B., Yee, H.C.:Construction of conservative numerical fluxes for the entropy split method. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-020-00111-4
17. Titarev, V.A., Toro, E.F.:ADER:arbitrary high order Godunov approach. J. Sci. Comput. 17, 609-618 (2002)
18. Toro, E.F., Millington, R.C., Nejad, L.A.M.:Towards very high-order Godunov schemes. In:Toro, E.F. (ed.) Godunov Methods:Theory and Applications, pp. 905-937. Kluwer Academic/Plenum Publishers, London (2001)
19. Toro, E.F., Titarev, V.A.:Solution of the generalised Riemann problem for advection-reaction equations. Proc. Roy. Soc. Lond. A 458, 271-281 (2002)
20. Toro, E.F., Santacá, A., Montecinos, G.I., Celant, M., Müller, L.O.:AENO:a novel reconstruction method in conjunction with ADER schemes for hyperbolic equations. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00147-0
21. Zeifang, J., Beck, A.:A low Mach number IMEX flux splitting for the level set ghost fluid method. Commun. Appl. Math. Comput. (2021). https://doi.org/10.1007/s42967-021-00137-2
