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Volumn 19, Issue 4, 1998, Pages 1261-1289

Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity

Author keywords

Adaptivity; Differential equations; Equidistribution; Pseudospectral

Indexed keywords


EID: 0000990612     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595291984     Document Type: Article
Times cited : (37)

References (28)
  • 1
    • 0039215744 scopus 로고
    • An adaptive pseudospectral method for discontinuous problems
    • J. M. AUGENBAUM, An adaptive pseudospectral method for discontinuous problems, Appl. Numer. Math., 5 (1989), pp. 459-480.
    • (1989) Appl. Numer. Math. , vol.5 , pp. 459-480
    • Augenbaum, J.M.1
  • 3
    • 0001334450 scopus 로고
    • An adaptive pseudospectrai method for reaction diffusion problems
    • A. BAYLISS, D. GOTTLIEB, B. MATKOWSKY, AND M. MINKOFF, An adaptive pseudospectrai method for reaction diffusion problems, J. Comput. Phys., 81 (1989), pp. 421-443.
    • (1989) J. Comput. Phys. , vol.81 , pp. 421-443
    • Bayliss, A.1    Gottlieb, D.2    Matkowsky, B.3    Minkoff, M.4
  • 4
    • 0001549875 scopus 로고
    • Fronts, relaxation oscillations and period doubling in solid fuel combustion
    • A. BAYLISS AND B. MATKOWSKY, Fronts, relaxation oscillations and period doubling in solid fuel combustion, J. Comput. Phys., 71 (1987), pp. 147-188.
    • (1987) J. Comput. Phys. , vol.71 , pp. 147-188
    • Bayliss, A.1    Matkowsky, B.2
  • 5
    • 28144442068 scopus 로고
    • Mappings and accuracy for Chebyshev pseudospectral approximations
    • A. BAYLISS AND E. TURKEL, Mappings and accuracy for Chebyshev pseudospectral approximations, J. Comput. Phys., 101 (1992), pp. 349-359.
    • (1992) J. Comput. Phys. , vol.101 , pp. 349-359
    • Bayliss, A.1    Turkel, E.2
  • 6
    • 49049134162 scopus 로고
    • Adaptive zoning for singular problems in two dimensions
    • J. U. BRACKBILL AND J. S. SALTZMAN, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys., 46 (1982), pp. 342-368.
    • (1982) J. Comput. Phys. , vol.46 , pp. 342-368
    • Brackbill, J.U.1    Saltzman, J.S.2
  • 7
    • 84966236671 scopus 로고
    • Essentially nonoscillatory spectral Fourier methods for shock wave calculation
    • W. CAI, D. GOTTLIEB, AND C.-W. SHU, Essentially nonoscillatory spectral Fourier methods for shock wave calculation, Math. Comput., 52 (1989), pp. 389-410.
    • (1989) Math. Comput. , vol.52 , pp. 389-410
    • Cai, W.1    Gottlieb, D.2    Shu, C.-W.3
  • 8
    • 0026907997 scopus 로고
    • On one-sided filters for spectral Fourier approximation of discontinuous functions
    • W. CAI, D. GOTTLIEB, AND C.-W. SHU, On one-sided filters for spectral Fourier approximation of discontinuous functions, SIAM J. Numer. Anal., 29 (1992), pp. 905-916.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 905-916
    • Cai, W.1    Gottlieb, D.2    Shu, C.-W.3
  • 10
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • E. A. DORFI AND L. O'C. DRURY, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys., 69 (1987), pp. 175-195.
    • (1987) J. Comput. Phys. , vol.69 , pp. 175-195
    • Dorfi, E.A.1    Drury, L.O'C.2
  • 11
    • 84974325250 scopus 로고
    • A review of PS methods for solving PDEs
    • B. FORNBERG AND D. M. SLOAN, A review of PS methods for solving PDEs, Acta Numerica, (1994), pp. 203-267.
    • (1994) Acta Numerica , pp. 203-267
    • Fornberg, B.1    Sloan, D.M.2
  • 12
    • 0000501465 scopus 로고
    • Spectral calculations in one-dimensional inviscid compressible flow
    • D. GOTTLIEB, L. LUSTMAN, AND S. A. ORSZAG, Spectral calculations in one-dimensional inviscid compressible flow, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 296-310.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 296-310
    • Gottlieb, D.1    Lustman, L.2    Orszag, S.A.3
  • 14
    • 0023861129 scopus 로고
    • On the use of spectral methods for the numerical solution of stiff problems
    • H. GUILLARD AND R. PEYRET, On the use of spectral methods for the numerical solution of stiff problems, Comput. Meth. Appl. Mech. Engrg., 66 (1988), pp. 17-43.
    • (1988) Comput. Meth. Appl. Mech. Engrg. , vol.66 , pp. 17-43
    • Guillard, H.1    Peyret, R.2
  • 15
    • 0000664743 scopus 로고
    • Review of some adaptive node-movement techniques in finite element and finite difference solutions of PDEs
    • D. F. HAWKEN, J. J. GOTTLIEB, AND J. S. HANSEN, Review of some adaptive node-movement techniques in finite element and finite difference solutions of PDEs, J. Comput. Phys., 95 (1991), pp. 254-302.
    • (1991) J. Comput. Phys. , vol.95 , pp. 254-302
    • Hawken, D.F.1    Gottlieb, J.J.2    Hansen, J.S.3
  • 16
    • 11744284075 scopus 로고
    • Analysis of Moving Mesh PDEs with Spatial Smoothing
    • Simon Fraser University, Burnaby, BC
    • W.-Z. HUANG AND R. D. RUSSELL, Analysis of Moving Mesh PDEs with Spatial Smoothing, Simon Fraser Mathematics Research Report, Simon Fraser University, Burnaby, BC, 1993, pp. 93-17.
    • (1993) Simon Fraser Mathematics Research Report , pp. 93-117
    • Huang, W.-Z.1    Russell, R.D.2
  • 17
    • 21344483926 scopus 로고
    • A new pseudospectral method with upwind features
    • W.-Z. HUANG AND D. M. SLOAN, A new pseudospectral method with upwind features, IMA J. Numer. Anal., 13 (1993), pp. 413-430.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 413-430
    • Huang, W.-Z.1    Sloan, D.M.2
  • 18
    • 0001354685 scopus 로고
    • A simple adaptive grid method in two dimensions
    • W.-Z. HUANG AND D. M. SLOAN, A simple adaptive grid method in two dimensions, SIAM J. Sci. Comput., 15 (1994), pp. 776-797.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 776-797
    • Huang, W.-Z.1    Sloan, D.M.2
  • 19
    • 38249029472 scopus 로고
    • Monotone and comonotone polynomial approximation revisited
    • D. LEVIATAN, Monotone and comonotone polynomial approximation revisited, J. Approx. Theory, 53 (1988), pp. 1-16.
    • (1988) J. Approx. Theory , vol.53 , pp. 1-16
    • Leviatan, D.1
  • 20
    • 0001314782 scopus 로고    scopus 로고
    • The efficient generation of simple two-dimensional adaptive grids
    • to appear
    • J. A. MACKENZIE, The efficient generation of simple two-dimensional adaptive grids, SIAM J. Sci. Comput., (1998), to appear.
    • (1998) SIAM J. Sci. Comput.
    • Mackenzie, J.A.1
  • 21
    • 84912983533 scopus 로고
    • The Fourier method for non-smooth initial data
    • A. MAJDA, J. MCDONOUGH, AND S. OSHER, The Fourier method for non-smooth initial data, Math. Comput., 32 (1978), pp. 1041-1081.
    • (1978) Math. Comput. , vol.32 , pp. 1041-1081
    • Majda, A.1    Mcdonough, J.2    Osher, S.3
  • 22
    • 11744319058 scopus 로고
    • The effect of filtering on the pseudospectral solution of evolutionary partial differential equations
    • L. S. MULHOLLAND AND D. M. SLOAN, The effect of filtering on the pseudospectral solution of evolutionary partial differential equations, J. Comput. Phys., 96 (1991), pp. 369-390.
    • (1991) J. Comput. Phys. , vol.96 , pp. 369-390
    • Mulholland, L.S.1    Sloan, D.M.2
  • 23
    • 0002147664 scopus 로고
    • Convergence of spectral methods for nonlinear conservation laws
    • E. TADMOR, Convergence of spectral methods for nonlinear conservation laws, SIAM J. Numer. Anal., 26 (1989), pp. 30-44.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 30-44
    • Tadmor, E.1
  • 24
    • 0025448705 scopus 로고
    • Shock capturing by the spectral viscosity method
    • E. TADMOR, Shock capturing by the spectral viscosity method, Comput. Meth. Appl. Mech. Engrg., 80 (1990), pp. 197-208.
    • (1990) Comput. Meth. Appl. Mech. Engrg. , vol.80 , pp. 197-208
    • Tadmor, E.1
  • 25
    • 0026203648 scopus 로고
    • Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    • E. TADMOR, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations, SIAM J. Numer. Anal., 28 (1991), pp. 891-906.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 891-906
    • Tadmor, E.1
  • 26
    • 0001581262 scopus 로고    scopus 로고
    • Boundary layer resolving pseudospectral methods for singular perturbation problems
    • T. TANG AND M. R. TRUMMER, Boundary layer resolving pseudospectral methods for singular perturbation problems, SIAM J. Sci. Comput., 17 (1996), pp. 430-438.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 430-438
    • Tang, T.1    Trummer, M.R.2
  • 28
    • 0000342281 scopus 로고
    • On selection of equidistribution meshes for two-point boundary value problems
    • A. B. WHITE, On selection of equidistribution meshes for two-point boundary value problems, SIAM J. Numer. Anal., 16 (1979), pp. 472-502.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 472-502
    • White, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.