메뉴 건너뛰기




Volumn 24, Issue 1, 1997, Pages 61-79

Comparison of H and P finite element approximations of the shallow water equations

Author keywords

Adaptive refinement; Convergence; Finite element; Shallow water equations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; HARMONIC ANALYSIS; VELOCITY; WAVEFORM ANALYSIS;

EID: 0030970147     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19970115)24:1<61::AID-FLD479>3.0.CO;2-Y     Document Type: Review
Times cited : (7)

References (41)
  • 1
    • 0017450330 scopus 로고
    • On the calculation of tidal currents in homogeneous estuaries
    • C. E. Pearson and D. F. Winter, 'On the calculation of tidal currents in homogeneous estuaries', J. Phys. Oceanogr., 7, 520 (1977).
    • (1977) J. Phys. Oceanogr. , vol.7 , pp. 520
    • Pearson, C.E.1    Winter, D.F.2
  • 2
    • 0018327004 scopus 로고
    • A study of tides, setup, and bottom friction in a shallow semi-enclosed basin. Part II: Tidal model and comparison with data
    • R. L. Snyder, M. Sidjabat and J. H. Filloux, 'A study of tides, setup, and bottom friction in a shallow semi-enclosed basin. Part II: Tidal model and comparison with data', J. Phys. Oceanogr., 9, 170-188 (1979).
    • (1979) J. Phys. Oceanogr. , vol.9 , pp. 170-188
    • Snyder, R.L.1    Sidjabat, M.2    Filloux, J.H.3
  • 3
    • 0018514925 scopus 로고
    • A wave equation model for finite element tidal computations
    • D. R. Lynch and W. G. Gray, 'A wave equation model for finite element tidal computations', Comput. Fluids, 7, 207-228 (1979).
    • (1979) Comput. Fluids , vol.7 , pp. 207-228
    • Lynch, D.R.1    Gray, W.G.2
  • 4
    • 0019376082 scopus 로고
    • Numerical modelling of the harmonic constituents of the tides, with application to the English Channel
    • C. Le Provost, G. Rougier and A. Poncet, 'Numerical modelling of the harmonic constituents of the tides, with application to the English Channel', J. Phys. Oceanogr., 11, 1123-1138 (1981).
    • (1981) J. Phys. Oceanogr. , vol.11 , pp. 1123-1138
    • Le Provost, C.1    Rougier, G.2    Poncet, A.3
  • 5
    • 0017830247 scopus 로고
    • Periodic Galerkin finite element method of tidal flow
    • M. Kawahara and K. Hasegawa, 'Periodic Galerkin finite element method of tidal flow', Int. j. numer methods eng., 12, 115 (1978).
    • (1978) Int. J. Numer Methods Eng. , vol.12 , pp. 115
    • Kawahara, M.1    Hasegawa, K.2
  • 6
    • 0023107743 scopus 로고
    • Three dimensional hydrodynamics on finite elements. Part 1: Linearized harmonic model
    • D. R. Lynch and F. E. Werner, 'Three dimensional hydrodynamics on finite elements. Part 1: Linearized harmonic model', Int. j. numer. methods fluids, 7, 871-909 (1987).
    • (1987) Int. J. Numer. Methods Fluids , vol.7 , pp. 871-909
    • Lynch, D.R.1    Werner, F.E.2
  • 7
    • 0026416607 scopus 로고
    • Three dimensional hydrodynamics on finite elements. Part 2: Nonlinear time stepping model
    • D. R. Lynch and F. E. Werner, 'Three dimensional hydrodynamics on finite elements. Part 2: Nonlinear time stepping model', Int. j. numer methods fluids, 12, 507-533 (1991).
    • (1991) Int. J. Numer Methods Fluids , vol.12 , pp. 507-533
    • Lynch, D.R.1    Werner, F.E.2
  • 8
    • 0023416425 scopus 로고
    • A model for tides and currents in the English Channel and southern North Sea
    • R. A. Walters, 'A model for tides and currents in the English Channel and southern North Sea', Adv. Water Res., 10, 138-148 (1987).
    • (1987) Adv. Water Res. , vol.10 , pp. 138-148
    • Walters, R.A.1
  • 9
    • 0003121009 scopus 로고
    • A three-dimensional, finite element model for coastal and estuarine circulation
    • R. A. Walters, 'A three-dimensional, finite element model for coastal and estuarine circulation', Continental Shelf Res., 12, 83-102 (1992).
    • (1992) Continental Shelf Res. , vol.12 , pp. 83-102
    • Walters, R.A.1
  • 10
    • 0027084283 scopus 로고
    • A three-dimensional, finite element model for baroclinic circulation on the Vancouver Island continental shelf
    • R. A. Walters and M. G. G. Foreman, 'A three-dimensional, finite element model for baroclinic circulation on the Vancouver Island continental shelf', J. Marine Syst., 3, 507-518 (1992).
    • (1992) J. Marine Syst. , vol.3 , pp. 507-518
    • Walters, R.A.1    Foreman, M.G.G.2
  • 11
    • 0023526496 scopus 로고
    • A primitive pseudo wave equation formulation for solving the harmonic shallow water equations
    • J. J. Westerink, J. J. Conner and K. D. Stolzenbach, 'A primitive pseudo wave equation formulation for solving the harmonic shallow water equations', Adv. Water Res., 10, 188-199 (1987).
    • (1987) Adv. Water Res. , vol.10 , pp. 188-199
    • Westerink, J.J.1    Conner, J.J.2    Stolzenbach, K.D.3
  • 12
    • 0001311706 scopus 로고
    • Progress in surface water modelling
    • J. J. Westerink and W. G. Gray, 'Progress in surface water modelling', Rev. Geophys., Suppl., April, 201-217 (1991).
    • (1991) Rev. Geophys., Suppl. , vol.APRIL , pp. 201-217
    • Westerink, J.J.1    Gray, W.G.2
  • 13
    • 0013725231 scopus 로고
    • Accuracy of an estuarine hydrodynamic model using smooth elements
    • R. A. Walters and R. T. Chen, 'Accuracy of an estuarine hydrodynamic model using smooth elements', Water Resources Res., 16, 187-195 (1980).
    • (1980) Water Resources Res. , vol.16 , pp. 187-195
    • Walters, R.A.1    Chen, R.T.2
  • 14
    • 0020850443 scopus 로고
    • Numerically induced oscillations in finite element approximations to the shallow water equations
    • R. A. Walters, 'Numerically induced oscillations in finite element approximations to the shallow water equations', Int. j. numer. methods fluids, 3, 591-604 (1983).
    • (1983) Int. J. Numer. Methods Fluids , vol.3 , pp. 591-604
    • Walters, R.A.1
  • 15
    • 38249039023 scopus 로고
    • Some tests of precision for a finite element model of ocean tides
    • C. Le Provost and P. Vincent, 'Some tests of precision for a finite element model of ocean tides', J. Comput. Phys., 65, 273-291 (1986).
    • (1986) J. Comput. Phys. , vol.65 , pp. 273-291
    • Le Provost, C.1    Vincent, P.2
  • 17
    • 0001759083 scopus 로고
    • The p-version of the finite element method
    • I. Babuska, B. A. Szabo and I. N. Katz, 'The p-version of the finite element method', SIAM J. Numer. And., 18, 515-544 (1981).
    • (1981) SIAM J. Numer. And. , vol.18 , pp. 515-544
    • Babuska, I.1    Szabo, B.A.2    Katz, I.N.3
  • 18
    • 0000808028 scopus 로고
    • The p version of the finite element method for domains with curved boundaries
    • I. Babuska and B. Guo, 'The p version of the finite element method for domains with curved boundaries', SIAM J. Numer. Anal., 25, 837-861 (1988).
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 837-861
    • Babuska, I.1    Guo, B.2
  • 19
    • 0000026672 scopus 로고
    • The h - P version of the finite element method with quasiuniform meshes
    • I. Babuska and M. Suri, 'the h - p version of the finite element method with quasiuniform meshes', Math. Mod. Numer. Anal., 21, 199-238 (1987).
    • (1987) Math. Mod. Numer. Anal. , vol.21 , pp. 199-238
    • Babuska, I.1    Suri, M.2
  • 20
    • 0026205720 scopus 로고
    • hp adaptive finite element methods in computational fluid dynamics
    • J. T. Oden and L. Demkowicz, 'hp adaptive finite element methods in computational fluid dynamics', Comput. Methods Appl. Mech. Eng., 89, 11-40 (1991).
    • (1991) Comput. Methods Appl. Mech. Eng. , vol.89 , pp. 11-40
    • Oden, J.T.1    Demkowicz, L.2
  • 21
    • 0029102509 scopus 로고
    • An hp adaptive strategy for finite element approximations of the Navier-Stokes equations
    • J. T. Oden, W. Wu and V. Legat, 'An hp adaptive strategy for finite element approximations of the Navier-Stokes equations', Int. j. numer. methods fluids, 20, 831-851 (1995).
    • (1995) Int. J. Numer. Methods Fluids , vol.20 , pp. 831-851
    • Oden, J.T.1    Wu, W.2    Legat, V.3
  • 22
    • 0025684066 scopus 로고
    • A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and hp adaptivity
    • L. Demkowicz, J. T. Oden and W. Rachowicz, 'A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and hp adaptivity', Comput. Methods Appl. Mech. Eng., 84, 275-326 (1990).
    • (1990) Comput. Methods Appl. Mech. Eng. , vol.84 , pp. 275-326
    • Demkowicz, L.1    Oden, J.T.2    Rachowicz, W.3
  • 24
    • 48549109395 scopus 로고
    • A spectral element method for fluid dynamics; laminar flow in a channel expansion
    • A. T. Patera, 'A spectral element method for fluid dynamics; laminar flow in a channel expansion', J. Comput. Phys., 54, 468-477 (1984).
    • (1984) J. Comput. Phys. , vol.54 , pp. 468-477
    • Patera, A.T.1
  • 25
    • 0038679072 scopus 로고
    • Spectral and pseudo spectral approximations of the Navier Stokes equations
    • Y. Maday and A. Quarteroni, 'Spectral and pseudo spectral approximations of the Navier Stokes equations', SIAM J. Numer. Anal., 19, 761-780 (1982).
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 761-780
    • Maday, Y.1    Quarteroni, A.2
  • 26
    • 0028450352 scopus 로고
    • Spectral element method for large scale parallel Navier-Stokes calculations
    • P. Fischer and E. Ronquist, 'Spectral element method for large scale parallel Navier-Stokes calculations', Comput. Methods Appl. Mech. Eng., 116, 69-76 (1994).
    • (1994) Comput. Methods Appl. Mech. Eng. , vol.116 , pp. 69-76
    • Fischer, P.1    Ronquist, E.2
  • 27
    • 0028976599 scopus 로고
    • A staggered spectral element model with application to the oceanic shallow water equations
    • M. Iskandarani, D. Haidvogel and J. Boyd, 'A staggered spectral element model with application to the oceanic shallow water equations', Int. j. numer. methods fluids, 20, 393-414 (1995).
    • (1995) Int. J. Numer. Methods Fluids , vol.20 , pp. 393-414
    • Iskandarani, M.1    Haidvogel, D.2    Boyd, J.3
  • 28
    • 0001272090 scopus 로고
    • A spectral element basin model for the shallow water equations
    • H. Ma, 'A spectral element basin model for the shallow water equations', J. Comput. Phys., 109, 133-149 (1993).
    • (1993) J. Comput. Phys. , vol.109 , pp. 133-149
    • Ma, H.1
  • 29
    • 6044258324 scopus 로고    scopus 로고
    • A model study of tidal and residual circulation in Delaware Bay and River
    • in press
    • R. A. Walters, 'A model study of tidal and residual circulation in Delaware Bay and River', J. Geophys. Res., in press.
    • J. Geophys. Res.
    • Walters, R.A.1
  • 30
    • 0000800022 scopus 로고
    • On the pressure gradient force over steep topography in sigma coordinate ocean models
    • R. L. Haney, On the pressure gradient force over steep topography in sigma coordinate ocean models', J. Phys. Oceanogr., 21, 610-619 (1991).
    • (1991) J. Phys. Oceanogr. , vol.21 , pp. 610-619
    • Haney, R.L.1
  • 32
    • 0028887261 scopus 로고
    • A tidal model for eastern Juan de Fuca Strait and the southern Strait of Georgie
    • M. G. G. Foreman, R. A. Walters, R. F. Henry, C. P. Keller and A. G. Dolling, 'A tidal model for eastern Juan de Fuca Strait and the southern Strait of Georgie', J. Geophys. Res., 100(C1), 721-740 (1995).
    • (1995) J. Geophys. Res. , vol.100 , Issue.C1 , pp. 721-740
    • Foreman, M.G.G.1    Walters, R.A.2    Henry, R.F.3    Keller, C.P.4    Dolling, A.G.5
  • 33
    • 0027629127 scopus 로고
    • A geometrically-based, automatic generator for irregular triangular networks
    • R. F. Henry and R. A. Walters, 'A geometrically-based, automatic generator for irregular triangular networks', Commun. Numer. Methods Eng., 9, 555-566 (1993).
    • (1993) Commun. Numer. Methods Eng. , vol.9 , pp. 555-566
    • Henry, R.F.1    Walters, R.A.2
  • 34
    • 0000916087 scopus 로고
    • The h, p, h-p version of FEM for 1-d problem: 1 p error analysis, II h, h - P error analysis, III Adaptive h - p
    • I. Babuska and B. Guo, 'The h, p, h-p version of FEM for 1-d problem: 1 p error analysis, II h, h - p error analysis, III Adaptive h - p', Numer. Math., 49, 577-683 (1986).
    • (1986) Numer. Math. , vol.49 , pp. 577-683
    • Babuska, I.1    Guo, B.2
  • 35
    • 6044255444 scopus 로고
    • h-p version FEM: I Basic approximation results, II General results
    • I. Babuska and B. Guo, 'h-p version FEM: I Basic approximation results, II General results', Comput. Mech., 1, 21-45 (1986).
    • (1986) Comput. Mech. , vol.1 , pp. 21-45
    • Babuska, I.1    Guo, B.2
  • 36
    • 0024885663 scopus 로고
    • Toward a universal hp adaptive finite element strategy, Part 3. Design of hp meshes
    • W. Rachowicz, J. T. Oden and L. Demkowicz, 'Toward a universal hp adaptive finite element strategy, Part 3. Design of hp meshes', Comput. Methods Appl. Mech. Eng., 77, 181-212 (1989).
    • (1989) Comput. Methods Appl. Mech. Eng. , vol.77 , pp. 181-212
    • Rachowicz, W.1    Oden, J.T.2    Demkowicz, L.3
  • 37
    • 0029277076 scopus 로고
    • A parallel adaptive stategy for hp finite element computations
    • J. T. Oden and A. Patra, 'A parallel adaptive stategy for hp finite element computations', Comput. Methods Appl. Mech. Eng., 121, 449-470 (1995).
    • (1995) Comput. Methods Appl. Mech. Eng. , vol.121 , pp. 449-470
    • Oden, J.T.1    Patra, A.2
  • 39
    • 0024945154 scopus 로고
    • Toward a universal hp adaptive finite element strategy, Part 2. A posterio error estimation
    • J. T. Oden, L. Demkowicz, W. Rachowicz and T. Westerman, 'Toward a universal hp adaptive finite element strategy, Part 2. A posterio error estimation', Comput. Methods Appl. Mech. Eng., 77, 113-180 (1989).
    • (1989) Comput. Methods Appl. Mech. Eng. , vol.77 , pp. 113-180
    • Oden, J.T.1    Demkowicz, L.2    Rachowicz, W.3    Westerman, T.4
  • 40
    • 0027790555 scopus 로고
    • Application of conjugate gradient methods to tidal simulation
    • E. Barragy, G. Carey and R. Walters, 'Application of conjugate gradient methods to tidal simulation', Adv. Water Res., 16, 163-171 (1993).
    • (1993) Adv. Water Res. , vol.16 , pp. 163-171
    • Barragy, E.1    Carey, G.2    Walters, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.