209
Views
2
CrossRef citations to date
0
Altmetric
Original Article

Galerkin–Legendre spectral method for Neumann boundary value problems in three dimensions

&
Pages 1335-1356 | Received 07 Sep 2017, Accepted 31 May 2018, Published online: 19 Jun 2018

References

  • F. Auteri and L. Quartapelle, Galerkin-Legendre spectral method for the 3D Helmholtz equation, J. Comput. Phys. 161 (2000), pp. 454–483. doi: 10.1006/jcph.2000.6504
  • F. Auteri, N. Parolini, and L. Quartapelle, Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers, J. Comput. Phys. 185 (2003), pp. 427–444. doi: 10.1016/S0021-9991(02)00064-5
  • C. Bernardi and Y. Maday, Spectral methods, in Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions, eds., Elsevier, Amsterdam, 1997, pp. 209–486.
  • J.P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed., Dover Publication Inc., Mineola, NY, 2001.
  • S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd ed., Springer-Verlag, Berlin, 2008.
  • C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin, 2006.
  • S.X. Chen, Introduction to Partial Differential Equations, People Education Press, Beijing, 1981.
  • M. Costabel and M. Dauge, A singularly perturbed mixed boundary value problem, Commun. Partial Differential Equations 21 (1996), pp. 1919–1949. doi: 10.1080/03605309608821249
  • M. Costabel, M. Dauge, and M. Surib, Numerical approximation of a singularly perturbed contact problem, Comput. Methods Appl. Mech. Engrg. 157 (1998), pp. 349–363. doi: 10.1016/S0045-7825(97)00245-4
  • A. Ezzirani and A. Guessab, A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations, Math. Comput. 68 (1999), pp. 217–248. doi: 10.1090/S0025-5718-99-01001-7
  • D. Funaro, A variational formulation for the Chebyshev pseudospectral approximation of Neumann problems, SIAM J. Numer. Anal. 27 (1990), pp. 695–703. doi: 10.1137/0727041
  • D. Funaro, Polynomial Approximations of Differential Equations, Springer-Verlag, Berlin, 1992.
  • D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS, Philadelphia, 1977.
  • P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, London, 1985.
  • B.Y. Guo, Spectral Methods and Their Applications, World Scientific, Singapore, 1998.
  • B.Y. Guo and T.J. Wang, Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an finite channel, Math. Comp. 78 (2009), pp. 129–151. doi: 10.1090/S0025-5718-08-02152-2
  • B.Y. Guo and T.J. Wang, Composite Laguerre-Legendre spectral method for exterior problems, Adv. Comput. Math. 32 (2010), pp. 393–429. doi: 10.1007/s10444-008-9112-5
  • B.Y. Guo and T.J. Wang, Composite Laguerre-Legendre spectral method for fourth-order exterior problems, J. Sci. Comput. 44 (2010), pp. 255–285. doi: 10.1007/s10915-010-9367-0
  • B.Y. Guo, J. Shen, and L.L. Wang, Optimal spectral-Galerkin methods using generalized Jacobi polynomials, J. Sci. Comput. 27 (2006), pp. 305–322. doi: 10.1007/s10915-005-9055-7
  • H.L. Jia and B.Y. Guo, Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons, Chin. Ann. Math. 31B (2010), pp. 855–878. doi: 10.1007/s11401-010-0614-3
  • L.S. Mulholland, W.Z. Huang, and D.M. Sloan, Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity, SIAM J. Sci. Comput. 19 (1998), pp. 1261–1289. doi: 10.1137/S1064827595291984
  • J. Shen, Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput. 15 (1994), pp. 1489–1505. doi: 10.1137/0915089
  • J. Shen, T. Tang, and L.L. Wang, Spectral Methods Algorithms Analysis and Applications, Springer-Verlag, Berlin, Heidelberg, 2011.
  • T. Sun and L.J. Yi, A Petrov-Galerkin spectral method for fourth-order problems, Math. Meth. Appl. Sci. 37 (2014), pp. 2257–2270. doi: 10.1002/mma.2973
  • Z.Q. Wang, The Laguerre spectral method for solving Neumann boundary value problems, J. Comput. Appl. Math. 235 (2011), pp. 3229–3237. doi: 10.1016/j.cam.2011.01.009
  • T.J. Wang, Mixed spectral method for heat transfer with inhomogeneous Neumann boundary condition in an infinite strip, Appl. Numer. Math. 92 (2015), pp. 82–97. doi: 10.1016/j.apnum.2015.01.010
  • T.J. Wang, A Spectral Method for Fourth-Order Mixed Inhomogeneous Boundary Value Problem in Three Dimensions, J. Sci. Comput. 67 (2016), pp. 1247–1271. doi: 10.1007/s10915-015-0106-4
  • T.J. Wang, Legendre spectral method for solving mixed boundary value problems on rectangle, Math. Meth. Appl. Sci. 39(13) (2016), pp. 3824–3835. doi: 10.1002/mma.3827
  • T.J. Wang and B.Y. Guo, Composite generalized Laguerre-Legendre pseudospectral method for Fokker-Planck equation in an infinite channel, Appl. Numer. Math. 58 (2008), pp. 1448–1466. doi: 10.1016/j.apnum.2007.08.007
  • T.J. Wang and B.Y. Guo, Composite Laguerre-Legendre pseudospectral method for exterior problems, Commun. Comput. Phys. 5 (2009), pp. 350–375.
  • T.J. Wang and Z.Q. Wang, Error analysis of Legendre spectral method with essential imposition of Neumann boundary condition, Appl. Numer. Math. 59 (2009), pp. 2444–2451. doi: 10.1016/j.apnum.2009.05.003
  • Z.Q. Wang and L.L. Wang, A collocation method with exact imposition of mixed boundary conditions, J. Sci. Comput. 42 (2010), pp. 291–317. doi: 10.1007/s10915-009-9325-x
  • T.J. Wang, B.Y. Guo, and W. Li, Spectral method for mixed inhomogeneous boundary value problems in three dimensions, J. Comput. Math. 30 (2012), pp. 579–600. doi: 10.4208/jcm.1206-m3891
  • X.H. Yu and Z.Q. Wang, Jacobi spectral method with essential imposition of Neumann boundary condition, Appl. Numer. Math. 62 (2012), pp. 956–974. doi: 10.1016/j.apnum.2012.03.004

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.