Open Access
Issue
ESAIM: M2AN
Volume 54, Number 6, November-December 2020
Page(s) 1917 - 1949
DOI https://doi.org/10.1051/m2an/2020025
Published online 16 September 2020
  1. C. Bardos, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d’approximation; application à l’équation de transport. Ann. Sci. Ec. Norm. Sup. Ser. 4 3 (1970) 185–233. [Google Scholar]
  2. H. Beirão Da Veiga, Existence results in Sobolev spaces for a stationary transport equation. Ricerche Mat. Suppl. XXXVI (1987) 173–184. [Google Scholar]
  3. S. Brenner and R. Scott, The Mathematical Theory of Finite Element Methods, 3rd ed.. Springer (2008). [Google Scholar]
  4. J. Coatléven, Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes. ESAIM: M2AN 49 (2015) 1063–1084. [EDP Sciences] [Google Scholar]
  5. J. Coatléven, A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes. ESAIM: M2AN 51 (2017) 797–824. [EDP Sciences] [Google Scholar]
  6. B. Cockburn, B. Dong and J. Guzmán, Optimal convergence of the original DG method for the transport-reaction equation on special meshes. SIAM J. Numer. Anal. 46 (2008) 1250–1265. [Google Scholar]
  7. D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. Springer (2012). [Google Scholar]
  8. R.J. DiPerna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
  9. R.H. Erskine, T.R. Green, J.A. Ramirez and L.H. MacDonald, Comparison of grid-based algorithms for computing upslope contributing area. Water Resour. Res. 42 (2006) W09416. [Google Scholar]
  10. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, edited by P.G. Ciarlet and J.-L. Lions. In: Handbook of Numerical Analysis: Techniques of Scientific Computing, Part III. North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
  11. R. Eymard, T. Gallouët and R. Herbin, A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis. C. R. Math. Acad. Sci. Paris 344 (2007) 403–406. [Google Scholar]
  12. R. Eymard, T. Gallouët and R. Herbin, Discretisation of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilisation and hybrid interfaces. IMA J. Numer. Anal. 30 (2010) 1009–1043. [Google Scholar]
  13. R. Eymard, C. Guichard and R. Herbin, Benchmark 3D: the vag scheme. In: Vol. 2 of Springer Proceedings in Mathematics, FVCA6, Prague (2011) 213–222. [Google Scholar]
  14. R. Eymard, C. Guichard and R. Herbin, Small-stencil 3D schemes for diffusive flows in porous media. ESAIM: M2AN 46 (2011) 265–290. [Google Scholar]
  15. E. Fernández-Cara, F. Guillén, R.R. Ortega, Mathematical modeling and analysis of visco-elastic fluids of the oldroyd kind, edited by P.G. Ciarlet and J.L. Lions. In: Vol. VIII of Handbook of Numerical Analysis: Numerical Methods for Fluids, Part 2. North-Holland, Amsterdam (2002) 543–661. [Google Scholar]
  16. T.G. Freeman, Calculating catchment area with divergent flow based on a regular grid. Comput. Geosci. 17 (1991) 413–422. [Google Scholar]
  17. V. Girault and L. Tartar, lp and w1,p regularity of the solution of a steady transport equation. C. R. Acad. Sci. Paris, Ser. I 348 (2010) 885–890. [Google Scholar]
  18. P. Holmgren, Multiple flow direction algorithms for runoff modelling in grid based elevation models: an empirical evaluation. Hydrol. Process. 8 (1994) 327–334. [Google Scholar]
  19. C. Johnson, J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comput. 46 (1986) 1–26. [Google Scholar]
  20. P. Lesaint and P.A. Raviart, On a finite element method for solving the neutron transport equation. Publ. Math. Inf. Rennes S 4 (1974) 1–40. [Google Scholar]
  21. C. Qin, A.-X. Zhu, T. Pei, B. Li, C. Zhou and L. Yang, An adaptive approach to selecting a flow-partition exponent for a multiple-flow-direction algorithm. Int. J. Geog. Inf. Sci. 21 (2007) 443–458. [Google Scholar]
  22. P. Quinn, K. Beven, P. Chevallier snd O. Planchon, The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models. Hydrol. Process. 5 (1991) 59–79. [Google Scholar]
  23. A. Richardson, C.N. Hill and J.T. Perron, IDA: an implicit, parallelizable method for calculating drainage area. Water Resour. Res. 50 (2013) 4110–4130. [Google Scholar]
  24. J. Seibert and B.L. McGlynn, A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models. Water Resour. Res. 43 (2007) W04501. [Google Scholar]
  25. D.G. Tarboton, A new method for the determination of flow directions and upslope areas in grid digital elevation models, Water Resour. Res. 33 (1997) 309–319. [Google Scholar]
  26. D.M. Wolock and G.J. McCabe Jr, Comparison of single and multiple flow direction algorithms for computing topographic parameters in topmodel, Water Resour. Res. 31 (1995) 1315–1324. [Google Scholar]
  27. Q. Zhou, P. Pilesjö and Y. Chen, Estimating surface flow paths on a digital elevation model using a triangular facet network, Water Resour. Res. 47 (2011) W07522. [Google Scholar]

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