메뉴 건너뛰기




Volumn 196, Issue 37-40 SPEC. ISS., 2007, Pages 3785-3797

Legendre and Chebyshev dual-Petrov-Galerkin methods for Hyperbolic equations

Author keywords

Chebyshev polynomials; Dual Petrov Galerkin method; Hyperbolic problems; Legendre polynomials; Spectral and pseudo spectral approximations

Indexed keywords

APPROXIMATION THEORY; GALERKIN METHODS; NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING;

EID: 34447104401     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.10.031     Document Type: Article
Times cited : (27)

References (23)
  • 2
    • 0034404929 scopus 로고    scopus 로고
    • Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions
    • Babuška I., and Guo B. Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions. Numer. Math. 85 2 (2000) 219-255
    • (2000) Numer. Math. , vol.85 , Issue.2 , pp. 219-255
    • Babuška, I.1    Guo, B.2
  • 4
    • 0001397113 scopus 로고
    • Error estimates for spectral and pseudospectral approximations of hyperbolic equations
    • Canuto C., and Quarteroni A. Error estimates for spectral and pseudospectral approximations of hyperbolic equations. SIAM J. Numer. Anal. 19 3 (1982) 629-642
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.3 , pp. 629-642
    • Canuto, C.1    Quarteroni, A.2
  • 5
    • 0000359606 scopus 로고
    • Preconditioner minimal residual methods for Chebyshev spectral calculations
    • Canuto C., and Quarteroni A. Preconditioner minimal residual methods for Chebyshev spectral calculations. J. Comput. Phys. 60 (1985) 315-337
    • (1985) J. Comput. Phys. , vol.60 , pp. 315-337
    • Canuto, C.1    Quarteroni, A.2
  • 8
    • 21344494565 scopus 로고
    • On the stability of the unsmoothed Fourier method for hyperbolic equations
    • Goodman J., Hou T., and Tadmor E. On the stability of the unsmoothed Fourier method for hyperbolic equations. Numer. Math. 67 1 (1994) 93-129
    • (1994) Numer. Math. , vol.67 , Issue.1 , pp. 93-129
    • Goodman, J.1    Hou, T.2    Tadmor, E.3
  • 9
    • 0035281653 scopus 로고    scopus 로고
    • Spectral methods for hyperbolic problems
    • Numerical analysis 2000, vol. VII, Partial differential equations
    • Gottlieb D., and Hesthaven J.S. Spectral methods for hyperbolic problems. J. Comput. Appl. Math. 128 1-2 (2001) 83-131 Numerical analysis 2000, vol. VII, Partial differential equations
    • (2001) J. Comput. Appl. Math. , vol.128 , Issue.1-2 , pp. 83-131
    • Gottlieb, D.1    Hesthaven, J.S.2
  • 11
    • 84966248629 scopus 로고
    • The stability of pseudospectral-Chebyshev methods
    • Gottlieb D. The stability of pseudospectral-Chebyshev methods. Math. Comp. 36 153 (1981) 107-118
    • (1981) Math. Comp. , vol.36 , Issue.153 , pp. 107-118
    • Gottlieb, D.1
  • 12
    • 84966257131 scopus 로고
    • The CFL condition for spectral approximations to hyperbolic initial-boundary value problems
    • Gottlieb D., and Tadmor E. The CFL condition for spectral approximations to hyperbolic initial-boundary value problems. Math. Comp. 56 194 (1991) 565-588
    • (1991) Math. Comp. , vol.56 , Issue.194 , pp. 565-588
    • Gottlieb, D.1    Tadmor, E.2
  • 13
    • 34447102560 scopus 로고    scopus 로고
    • On the dual Petrov-Galerkin formulation of the KDV equation in a finite interval
    • Goubet O., and Shen J. On the dual Petrov-Galerkin formulation of the KDV equation in a finite interval. Adv. Diff. Eqn. 12 (2007) 221-239
    • (2007) Adv. Diff. Eqn. , vol.12 , pp. 221-239
    • Goubet, O.1    Shen, J.2
  • 14
    • 3543090402 scopus 로고    scopus 로고
    • Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
    • Guo B.-y., and Wang L.-l. Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces. J. Approx. Theory 128 1 (2004) 1-41
    • (2004) J. Approx. Theory , vol.128 , Issue.1 , pp. 1-41
    • Guo, B.-y.1    Wang, L.-l.2
  • 15
    • 33745038998 scopus 로고    scopus 로고
    • Optimal spectral-galerkin methods using generalized jacobi polynomials
    • Guo B., Shen J., and Wang L.-L. Optimal spectral-galerkin methods using generalized jacobi polynomials. J. Sci. Comput. (2006)
    • (2006) J. Sci. Comput.
    • Guo, B.1    Shen, J.2    Wang, L.-L.3
  • 16
    • 0346009114 scopus 로고    scopus 로고
    • Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation
    • Jackiewicz Z., and Welfert B.D. Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation. J. Sci. Comput. 18 2 (2003) 287-313
    • (2003) J. Sci. Comput. , vol.18 , Issue.2 , pp. 287-313
    • Jackiewicz, Z.1    Welfert, B.D.2
  • 17
    • 0000914453 scopus 로고
    • Comparison of accurate methods for the integration of hyperbolic equations
    • Kreiss H.-O., and Oliger J. Comparison of accurate methods for the integration of hyperbolic equations. Tellus 24 (1972) 199-215
    • (1972) Tellus , vol.24 , pp. 199-215
    • Kreiss, H.-O.1    Oliger, J.2
  • 18
    • 85013126603 scopus 로고
    • Spectral methods for complex geometries
    • Orszag S.A. Spectral methods for complex geometries. J. Comput. Phys. 37 (1980) 70-92
    • (1980) J. Comput. Phys. , vol.37 , pp. 70-92
    • Orszag, S.A.1
  • 19
    • 0035733976 scopus 로고    scopus 로고
    • Preconditioning Legendre spectral collocation methods for elliptic problems. II. Finite element operators
    • (electronic)
    • Parter S.V. Preconditioning Legendre spectral collocation methods for elliptic problems. II. Finite element operators. SIAM J. Numer. Anal. 39 1 (2001) 348-362 (electronic)
    • (2001) SIAM J. Numer. Anal. , vol.39 , Issue.1 , pp. 348-362
    • Parter, S.V.1
  • 20
    • 0000567049 scopus 로고
    • Efficient spectral-Galerkin method I. direct solvers for second- and fourth-order equations by using Legendre polynomials
    • Shen J. Efficient spectral-Galerkin method I. direct solvers for second- and fourth-order equations by using Legendre polynomials. SIAM J. Sci. Comput. 15 (1994) 1489-1505
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1489-1505
    • Shen, J.1
  • 21
    • 0002543392 scopus 로고
    • Efficient spectral-Galerkin method II. direct solvers for second- and fourth-order equations by using Chebyshev polynomials
    • Shen J. Efficient spectral-Galerkin method II. direct solvers for second- and fourth-order equations by using Chebyshev polynomials. SIAM J. Sci. Comput. 16 (1995) 74-87
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 74-87
    • Shen, J.1
  • 22
    • 9244255255 scopus 로고    scopus 로고
    • A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KDV equation
    • Shen J. A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KDV equation. SIAM J. Numer. Anal. 41 (2003) 1595-1619
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1595-1619
    • Shen, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.