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All issues Volume 308 (2021) E3S Web Conf., 308 (2021) 01020 References
Open Access
Issue
E3S Web Conf.
Volume 308, 2021
2021 6th International Conference on Materials Science, Energy Technology and Environmental Engineering (MSETEE 2021)
Article Number 01020
Number of page(s) 7
Section Energy Resource Development and Energy Saving Technology
DOI https://doi.org/10.1051/e3sconf/202130801020
Published online 27 September 2021
  1. A. T. Benjamin and D. Walton. Combinatorially composing Chebyshev polynomials. Journal of Statistical Planning and Inference, 140(8):2161–2167, aug 2010. [Google Scholar]
  2. J. P. Boyd. Chebyshev and Fourier Spectral Methods. New York, 2nd edition, 2000. 22 [Google Scholar]
  3. Bernardo Cockburn and Wang Chi-Shu. The Runge-Kutta discontinuous galerkin method for conservation laws V: Multidimensional systems. Technical Report TR97-43, (1997). [Google Scholar]
  4. Bernardo Cockburn and Chi-Wang Shu. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework. Math. Comput., 52, 411–435 (1989). [Google Scholar]
  5. Bernardo Cockburn and Chi-Wang Shu. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. SIAM J. Sci. Comput., 16, 173–261 (2001). [Google Scholar]
  6. B. Cockburn and C. W. Shu. The runge-kutta local projection p 1 -discontinuous Galerkin method for scalar conservation laws. M2AN., 25, 337–361 (1991). [Google Scholar]
  7. R. E. Caflisch. Monte Carlo and quasi-Monte Carlo methods. Acta Numerica, 7:1–49, 1998. [Google Scholar]
  8. Y. K. Cheung, W. G. Jin, and O. C. Zienkiewicz. Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions. Comm. Appl. Num. Meth., 5:159–169, 1989. [Google Scholar]
  9. J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297–297, may 1965. [Google Scholar]
  10. D. F. Griffiths, J. W. Dold, and D. J. Silvester. Separation of Variables. In Essential Partial Differential Equations, pages 129–159. Springer International Publishing, 2015. 39. [Google Scholar]
  11. R. Biswas, Karen D. Devine, and Joseph E. Flaherty. Parallel, adaptive finite element methods for conservation laws. Appl. Numer. Math., 14, 255–283 (1994). [Google Scholar]
  12. E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration, volume 31 of Spring Series in Computational Mathematics. Springer-Verlag, Berlin, Heidelberg, second edition. [Google Scholar]
  13. Johnson C. and Pitkaranta J. An analysis of the discontinuous Galerkin method. Math. Comput., 46, 1–26 (1986). [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Chavent and G. Salzano. A finite element method for the 1D water flooding problem with gravity. J. Comput. Phys., 45, 307–344 (1982). [Google Scholar]
  15. G. Chavent and B. Cockburn. The local projection p 0 p 1 -discontinuous-Galerkin method for scalar conservation laws. M2AN., 23, 565–592 (1989). [Google Scholar]
  16. B. van Leer. Towards the ultimate conservation difference scheme, V. J. Comput. Phys., 32, 1–136 (1979). [Google Scholar]
  17. C. W. Shu and S. Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys., 77, 439–471 (1988). [Google Scholar]
  18. C. E. Baumann and Oden J. T. A discontinuous hp finite element method for the solution of the Euler equation of gas dynamics. In 10th. International Conference on Finite Element in Fluids, (1998). [28] V. Aizinger, C. Dawson, B. Cockburn, and P. Castillo. Local discontinuous Galerkin method for contaminant transport. Advances in Water Resources., 24, 73–87 (2001). [Google Scholar]
  19. V. Aizinger, C. Dawson, B. Cockburn, and P. Castillo. Local discontinuous Galerkin method for contaminant transport. Advances in Water Resources., 24, 73–87 (2001). [Google Scholar]
  20. V. Aizinger and C. Dawson. A discontinuous Galerkin method for two-dimensional flow and transport in shallow water. Advances in Water Resources., 25, 67–84 (2002). [Google Scholar]
  21. Schwanenberg D. and Kongeter J. A discontinuous Galerkin methods for the shallow water equations with source terms. In CockburnB., Karniadakis G. E., and Shu C. W., editors, Discontinuous Galerkin Method, volume 11, pages 419–424. Springer, (2000). [Google Scholar]
  22. Bernardo Cockburn. Discontinuous Galerkin methods for convection-dominated problems. In Timothy J. Barth and Herman Deconinck, editors, High-Order Methods for Computational Physics, volume 9, pages 69–224. (1999). [Google Scholar]
  23. R. Biswas, Karen D. Devine, and Joseph E. Flaherty. Parallel, adaptive finite element methods for conservation laws. Appl. Numer. Math., 14, 255–283 (1994). [Google Scholar]
  24. Chi-Wang Shu. TVD time discretizations. SIAM J. Sci. Stat. Comput., 9, 1073–1084 (1988). [Google Scholar]
  25. J. P. Boyd. Chebyshev and Fourier Spectral Methods. New York, 2nd edition, 2000. [Google Scholar]
  26. B. Fornberg. A practical guide to pseudospectral methods. Cambridge University Press, Cambridge, 1996. 4, 23, 38. [Google Scholar]
  27. J. Fourier. Théorie analytique de la chaleur. Didot, Paris, 1822. 6, 31. [Google Scholar]
  28. M. Gisclon. A propos de l’équation de la chaleur et de l’analyse de Fourier. Le journal de maths des élèves, 1(4):190–197, 1998. 39 . [Google Scholar]
  29. D. F. Griffiths, J. W. Dold, and D. J. Silvester. Separation of Variables. In Essential Partial Differential Equations, pages 129–159. Springer International Publishing, 2015. 39. [Google Scholar]
  30. M. Chhay, D. Dutykh, M. Gisclon, and C. Ruyer-Quil. Asymptotic heat transfer model in thin liquid films. Submitted, pages 1–24, 2015. [Google Scholar]
  31. J. R. Dormand and P. J. Prince. A family of embedded Runge-Kutta formulae. J. Comp. Appl. Math., 6:19–26, 1980. [Google Scholar]
  32. A. Einstein. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 322(8):549–560, 1905. [Google Scholar]
  33. A. Einstein. Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes. Die Naturwissenschaften, 14(11):223–224, 1926. [Google Scholar]
  34. L. C. Evans. Partial Differential Equations. American Mathematical Society, Providence, Rhode Island, 2 edition, 2010. 29. [Google Scholar]

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