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Volumn 175, Issue 3-4, 1999, Pages 281-309

Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CHEBYSHEV APPROXIMATION; CONVERGENCE OF NUMERICAL METHODS; SPECTRUM ANALYSIS;

EID: 0033516456     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00358-2     Document Type: Article
Times cited : (43)

References (40)
  • 1
    • 0001019466 scopus 로고
    • The Dirichlet problem for the vibrating string equation
    • [1] D.G. Bourgin and R. Duffin, The Dirichlet problem for the vibrating string equation, Am. Math. Soc. Bull. 45 (1939) 851-858.
    • (1939) Am. Math. Soc. Bull. , vol.45 , pp. 851-858
    • Bourgin, D.G.1    Duffin, R.2
  • 3
    • 0042237868 scopus 로고
    • A lag-averaged generalization of Euler's method for accelerating series
    • [3] J.P. Boyd, A lag-averaged generalization of Euler's method for accelerating series, Appl. Math. Comput. 72 (1995) 143-166.
    • (1995) Appl. Math. Comput. , vol.72 , pp. 143-166
    • Boyd, J.P.1
  • 4
    • 0040361115 scopus 로고    scopus 로고
    • The Erfc-Log filter and the asymptotics of the Euler and Vandeven sum accelerations
    • A.V. Ilin and L.R. Scott, eds., Houston J. Mathematics, Houston, TX
    • [4] J.P. Boyd, The Erfc-Log filter and the asymptotics of the Euler and Vandeven sum accelerations, in: A.V. Ilin and L.R. Scott, eds., Proc. Third Int. Conf. on Spectral and High Order Methods (Houston J. Mathematics, Houston, TX, 1996) 267-276.
    • (1996) Proc. Third Int. Conf. on Spectral and High Order Methods ( , pp. 267-276
    • Boyd, J.P.1
  • 5
    • 77956861849 scopus 로고
    • New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly non-local solitary waves and numerical boundary value algorithms
    • T.-Y. Wu and J.W. Hutchinson, eds., Academic Press, New York
    • [5] J.P. Boyd, New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly non-local solitary waves and numerical boundary value algorithms, in: T.-Y. Wu and J.W. Hutchinson, eds., Advances in Applied Mechanics 27 (Academic Press, New York, 1989) 1-82.
    • (1989) Advances in Applied Mechanics , vol.27 , pp. 1-82
    • Boyd, J.P.1
  • 6
    • 0008977135 scopus 로고    scopus 로고
    • Construction of Lighthill's unitary functions: The imbricate series of unity
    • [6] J.P. Boyd, Construction of Lighthill's unitary functions: The imbricate series of unity, Appl. Math. Comput. 86 (1997) 1-10.
    • (1997) Appl. Math. Comput. , vol.86 , pp. 1-10
    • Boyd, J.P.1
  • 7
    • 0001750240 scopus 로고    scopus 로고
    • Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion
    • [7] J.P. Boyd, Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving boundary conditions and interpretation of the filter as a diffusion, J. Comput. Phys. 143 (1998) 283-288.
    • (1998) J. Comput. Phys. , vol.143 , pp. 283-288
    • Boyd, J.P.1
  • 9
    • 85040897227 scopus 로고
    • Cambridge University Press, New York
    • [9] R. Daley, Atmospheric Data Analysis (Cambridge University Press, New York, 1991).
    • (1991) Atmospheric Data Analysis
    • Daley, R.1
  • 10
    • 0021643764 scopus 로고
    • Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
    • [10] M. Deville, L. Kleiser and F. Montigny-Rannou, Pressure and time treatment for Chebyshev spectral solution of a Stokes problem, Int. J. Numer. Methods Fluids (1984) 1149-1163.
    • (1984) Int. J. Numer. Methods Fluids , pp. 1149-1163
    • Deville, M.1    Kleiser, L.2    Montigny-Rannou, F.3
  • 14
    • 33645807073 scopus 로고
    • Data assimilation in meteorology and oceanography
    • [14] M. Ghil and P. Malanotte-Rizzoli, Data assimilation in meteorology and oceanography, Adv. Geophys. 33 (1991) 141-266.
    • (1991) Adv. Geophys. , vol.33 , pp. 141-266
    • Ghil, M.1    Malanotte-Rizzoli, P.2
  • 16
    • 0031381548 scopus 로고    scopus 로고
    • On the Gibbs Phenomenon and its resolution
    • [16] D. Gottlieb and C.-W. Shu, On the Gibbs Phenomenon and its resolution, SIAM Rev. 39 (1997) 644-668.
    • (1997) SIAM Rev. , vol.39 , pp. 644-668
    • Gottlieb, D.1    Shu, C.-W.2
  • 17
    • 0022797838 scopus 로고
    • On pressure boundary conditions for the incompressible Navier-Stokes equations
    • [17] P.M. Gresho and R.L. Sani, On pressure boundary conditions for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 7 (1987) 1111-1145.
    • (1987) Int. J. Numer. Methods Fluids , vol.7 , pp. 1111-1145
    • Gresho, P.M.1    Sani, R.L.2
  • 18
    • 12044252810 scopus 로고
    • Incompressible fluid dynamics: Some fundamental formulation issues
    • [18] P.M. Gresho, Incompressible fluid dynamics: some fundamental formulation issues, Ann. Rev. Fluid Mech. 23 (1991) 413-453.
    • (1991) Ann. Rev. Fluid Mech. , vol.23 , pp. 413-453
    • Gresho, P.M.1
  • 19
    • 0026173203 scopus 로고
    • Some current CFD issues relevant to the incompressible Navier-Stokes equations
    • [19] P.M. Gresho, Some current CFD issues relevant to the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 87 (1991) 201-252.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.87 , pp. 201-252
    • Gresho, P.M.1
  • 20
    • 0006841592 scopus 로고    scopus 로고
    • Some interesting issues in incompressible fluid dynamics, both in the continuum and in numerical simulation
    • T.-Y. Wu and J.W. Hutchinson, eds., Academic Press, New York
    • [20] P.M. Gresho, Some interesting issues in incompressible fluid dynamics, both in the continuum and in numerical simulation, in: T.-Y. Wu and J.W. Hutchinson, eds., Advances in Applied Mechanics 28 (Academic Press, New York) 46-140.
    • Advances in Applied Mechanics , vol.28 , pp. 46-140
    • Gresho, P.M.1
  • 21
    • 49249143705 scopus 로고
    • The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
    • [21] D.B. Haidvogel and T.A. Zang, The accurate solution of Poisson's equation by expansion in Chebyshev polynomials, J. Comput. Phys. 30 (1979) 167-180.
    • (1979) J. Comput. Phys. , vol.30 , pp. 167-180
    • Haidvogel, D.B.1    Zang, T.A.2
  • 22
    • 0000966077 scopus 로고
    • Finite element approximation of the nonstationary Navier-Stokes problem. I: Regularity of the solutions and second-order error estimates for the spatial discretization
    • [22] J.C. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. I: Regularity of the solutions and second-order error estimates for the spatial discretization, SIAM J. of Numer. Anal. 19 (1982) 275-311.
    • (1982) SIAM J. of Numer. Anal. , vol.19 , pp. 275-311
    • Heywood, J.C.1    Rannacher, R.2
  • 23
    • 0022767064 scopus 로고
    • Finite element approximation of the nonstationary Navier-Stokes problem. II: Stability of solutions and error estimates uniform in time
    • [23] J.C. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. II: Stability of solutions and error estimates uniform in time, SIAM J. Numer. Anal. 23 (1986) 750-777.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 750-777
    • Heywood, J.C.1    Rannacher, R.2
  • 24
    • 0001510680 scopus 로고
    • The dirichlet problem for a hyperbolic equation
    • [24] F. John, The Dirichlet problem for a hyperbolic equation, Am. J. Math. 63 (1941) 141-154.
    • (1941) Am. J. Math. , vol.63 , pp. 141-154
    • John, F.1
  • 25
    • 0013173969 scopus 로고
    • On the convergence of Fourier series defining a solution of a mixed problem for hyperbolic equations
    • [25] O. Ladyzenskaja, On the convergence of Fourier series defining a solution of a mixed problem for hyperbolic equations, Dokl. Akad. Nauk. SSSR 85 (1952) 481-484.
    • (1952) Dokl. Akad. Nauk. SSSR , vol.85 , pp. 481-484
    • Ladyzenskaja, O.1
  • 26
    • 0013080536 scopus 로고
    • On the solvability of the fundamental boundary problems for equations of parabolic and hyperbolic type
    • [26] O. Ladyzenskaja, On the solvability of the fundamental boundary problems for equations of parabolic and hyperbolic type, Dokl. Akad. Nauk. SSSR 87 (1954) 395-398.
    • (1954) Dokl. Akad. Nauk. SSSR , vol.87 , pp. 395-398
    • Ladyzenskaja, O.1
  • 28
    • 0026493583 scopus 로고
    • Richardson's barotropic forecast: A reappraisal
    • [28] P. Lynch, Richardson's barotropic forecast: A reappraisal, Bull. Am. Met. Soc. 73 (1992) 35-47.
    • (1992) Bull. Am. Met. Soc. , vol.73 , pp. 35-47
    • Lynch, P.1
  • 29
    • 0000627077 scopus 로고
    • A spectral method for polar coordinates
    • [29] T. Matsushima and P.S. Marcus, A spectral method for polar coordinates, J. Comput. Phys. 120 (1995) 365-374.
    • (1995) J. Comput. Phys. , vol.120 , pp. 365-374
    • Matsushima, T.1    Marcus, P.S.2
  • 31
    • 77952889884 scopus 로고
    • Viscous and resistive eddies near a sharp corner
    • [31] H.K. Moffat, Viscous and resistive eddies near a sharp corner, J. Fluid Mech. 18 (1964) 1-18.
    • (1964) J. Fluid Mech. , vol.18 , pp. 1-18
    • Moffat, H.K.1
  • 32
    • 84967768753 scopus 로고
    • Differentiability of solutions to hyperbolic initial-boundary value problems
    • [32] J.B. Rauch and F.J. Massey, Differentiability of solutions to hyperbolic initial-boundary value problems, Trans. Am. Math. Soc. 189 (1974) 303-318.
    • (1974) Trans. Am. Math. Soc. , vol.189 , pp. 303-318
    • Rauch, J.B.1    Massey, F.J.2
  • 33
    • 0345257507 scopus 로고
    • Cambridge University Press, Cambridge, first published in Japanese in 1978
    • [33] R. Sakamoto, Hyperbolic Boundary Value Problems (Cambridge University Press, Cambridge, 1982) (first published in Japanese in 1978) 204.
    • (1982) Hyperbolic Boundary Value Problems , pp. 204
    • Sakamoto, R.1
  • 34
    • 2142850943 scopus 로고
    • Chebyshev pseudospectral method of viscous flows with corner singularities
    • [34] W.W. Schultz, N.Y. Lee and J.P. Boyd, Chebyshev pseudospectral method of viscous flows with corner singularities, J. Sci. Comput. 4(1) (1989) 1-24.
    • (1989) J. Sci. Comput. , vol.4 , Issue.1 , pp. 1-24
    • Schultz, W.W.1    Lee, N.Y.2    Boyd, J.P.3
  • 35
    • 51249184841 scopus 로고
    • Smooth solutions of the heat and diffusion equations
    • [35] S. Smale, Smooth solutions of the heat and diffusion equations, Comment. Math. Helvetici 55 (1980) 1-12.
    • (1980) Comment. Math. Helvetici , vol.55 , pp. 1-12
    • Smale, S.1
  • 36
    • 84968476219 scopus 로고
    • Numerical comparisons of nonlinear convergence accelerators
    • [36] D.A. Smith and W.F. Ford, Numerical comparisons of nonlinear convergence accelerators, Math. Comput. 38 (1982) 481-499.
    • (1982) Math. Comput. , vol.38 , pp. 481-499
    • Smith, D.A.1    Ford, W.F.2
  • 37
    • 0039990788 scopus 로고
    • Behaviour at time t = 0 of the solutions of semi-linear evolution equations
    • [37] R. Témam, Behaviour at time t = 0 of the solutions of semi-linear evolution equations, J. Diff. Eqns. 43 (1982) 73-92.
    • (1982) J. Diff. Eqns. , vol.43 , pp. 73-92
    • Témam, R.1
  • 38
    • 0343863901 scopus 로고
    • Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
    • [38] E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Rep. 10 (1989) 189-371.
    • (1989) Comput. Phys. Rep. , vol.10 , pp. 189-371
    • Weniger, E.J.1
  • 39
    • 0026141256 scopus 로고
    • On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series
    • [39] E.J. Weniger, On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Comm. 64 (1991) 19-45.
    • (1991) Comput. Phys. Comm. , vol.64 , pp. 19-45
    • Weniger, E.J.1


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