메뉴 건너뛰기




Volumn 25, Issue 3, 2003, Pages 815-831

Preconditioning methods for local discontinuous Galerkin discretizations

Author keywords

Finite elements; Local discontinuous Galerkin; Multigrid; Preconditioning; Saddle point problem

Indexed keywords

FINITE ELEMENT METHOD; ITERATIVE METHODS; LARGE SCALE SYSTEMS; MATHEMATICAL INSTRUMENTS; MATHEMATICAL MODELS; POISSON DISTRIBUTION; PROBLEM SOLVING;

EID: 2942574812     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502410657     Document Type: Article
Times cited : (29)

References (28)
  • 1
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • D. N. ARNOLD, An interior penalty finite element method with discontinuous elements, SIAM J. Numer. Anal., 19 (1982), pp. 742-760.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 2
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D. N. ARNOLD, F. BREZZI, B. COCKBURN, AND L. D. MARINI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2001), pp. 1749-1779.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 5
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • F. BASSI AND S. REBAY, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys., 131 (1997), pp. 267-279.
    • (1997) J. Comput. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0004219794 scopus 로고
    • Multigrid methods
    • Longman Scientific, Harlow, UK
    • J. H. BRAMBLE, Multigrid Methods, Pitman Res. Notes Math. Ser. 294, Longman Scientific, Harlow, UK, 1993.
    • (1993) Pitman Res. Notes Math. Ser. , vol.294
    • Bramble, J.H.1
  • 7
    • 0037252566 scopus 로고    scopus 로고
    • Performance of discontinuous Galerkin methods for elliptic PDEs
    • P. CASTILLO, Performance of discontinuous Galerkin methods for elliptic PDEs, SIAM J. Sci. Comput., 24 (2002), pp. 524-547.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 524-547
    • Castillo, P.1
  • 9
    • 0034548629 scopus 로고    scopus 로고
    • An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
    • P. CASTILLO, B. COCKBURN, I. PERUGIA, AND D. SCHÖTZAU, An a priori error analysis of the local discontinuous Galerkin method for elliptic problems, SIAM J. Numer. Anal., 38 (2000), pp. 1676-1706.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1676-1706
    • Castillo, P.1    Cockburn, B.2    Perugia, I.3    Schötzau, D.4
  • 10
    • 0036013520 scopus 로고    scopus 로고
    • An optimal a priori error estimate for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems
    • P. CASTILLO, B. COCKBURN, D. SCHÖTZAU, AND C. SCHWAB, An optimal a priori error estimate for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems, Math. Comput., 71 (2002), pp. 455-478.
    • (2002) Math. Comput. , vol.71 , pp. 455-478
    • Castillo, P.1    Cockburn, B.2    Schötzau, D.3    Schwab, C.4
  • 11
    • 0035734429 scopus 로고    scopus 로고
    • Superconvergence of the local discontinuous Galerkin method for elliptic problems on cartesian grids
    • B. COCKBURN, G. KANSCHAT, I. PERUGIA, AND D. SCHÖTZAU, Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids, SIAM J. Numer. Anal., 39 (2001), pp. 264-285.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 264-285
    • Cockburn, B.1    Kanschat, G.2    Perugia, I.3    Schötzau, D.4
  • 13
    • 4043055624 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for the Oseen equations
    • to appear
    • B. COCKBURN, G. KANSCHAT, AND D. SCHÖTZAU, The local discontinuous Galerkin method for the Oseen equations, Math. Comput., to appear.
    • Math. Comput.
    • Cockburn, B.1    Kanschat, G.2    Schötzau, D.3
  • 15
    • 0003979117 scopus 로고    scopus 로고
    • The development of discontinuous Galerkin methods
    • B. Cockburn, G. E. Karniadakis, and C.-W. Shu, eds., Springer, Berlin
    • B. COCKBURN, G. E. KARNIADAKIS, AND C.-W. SHU, The development of discontinuous Galerkin methods, in Discontinuous Galerkin Methods, B. Cockburn, G. E. Karniadakis, and C.-W. Shu, eds., Springer, Berlin, 2000, pp. 3-50.
    • (2000) Discontinuous Galerkin Methods , pp. 3-50
    • Cockburn, B.1    Karniadakis, G.E.2    Shu, C.-W.3
  • 17
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • B. COCKBURN AND C.-W. SHU, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal., 35 (1998), pp. 2440-2463.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 18
    • 0036003235 scopus 로고    scopus 로고
    • Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
    • H. C. ELMAN, D. J. SILVESTER, AND A. J. WATHEN, Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations, Numer. Math., 90 (2002), pp. 665-688.
    • (2002) Numer. Math. , vol.90 , pp. 665-688
    • Elman, H.C.1    Silvester, D.J.2    Wathen, A.J.3
  • 19
    • 0041419444 scopus 로고    scopus 로고
    • Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems
    • X. FENG AND O. A. KARAKASHIAN, Two-level additive Schwarz methods for a discontinuous Galerkin approximation of second order elliptic problems, SIAM J. Numer. Anal., 39 (2001), pp. 1343-1365.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1343-1365
    • Feng, X.1    Karakashian, O.A.2
  • 20
    • 0345060037 scopus 로고    scopus 로고
    • A multilevel discontinuous Galerkin method
    • J. GOPALAKRISHNAN AND G. KANSCHAT, A multilevel discontinuous Galerkin method, Numer. Math., 95 (2003), pp. 527-550.
    • (2003) Numer. Math. , vol.95 , pp. 527-550
    • Gopalakrishnan, J.1    Kanschat, G.2
  • 21
    • 2942610848 scopus 로고    scopus 로고
    • Multi-level preconditioners for the interior penalty method
    • F. Brezzi, A. Buffa, S. Corsaro, and A. Murli, eds., Springer Italia, Milan
    • J. GOPALAKRISHNAN AND G. KANSCHAT, Multi-level preconditioners for the interior penalty method, in Numerical Mathematics and Advanced Applications (ENUMATH 2001), F. Brezzi, A. Buffa, S. Corsaro, and A. Murli, eds., Springer Italia, Milan, 2003, pp. 795-804.
    • (2003) Numerical Mathematics and Advanced Applications (ENUMATH 2001) , pp. 795-804
    • Gopalakrishnan, J.1    Kanschat, G.2
  • 22
    • 85160628241 scopus 로고    scopus 로고
    • Practical aspects of multilevel preconditioned for discontinuous Galerkin methods with local refinement
    • SFB 359, Ruprecht-Karls University, Heidelberg, in preparation
    • G. KANSCHAT, Practical Aspects of Multilevel Preconditioned for Discontinuous Galerkin Methods with Local Refinement, Technical report, SFB 359, Ruprecht-Karls University, Heidelberg, in preparation.
    • Technical Report
    • Kanschat, G.1
  • 23
    • 0036992402 scopus 로고    scopus 로고
    • Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems
    • G. KANSCHAT AND R. RANNACHER, Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems, J. Numer. Math., 10 (2002), pp. 249-274.
    • (2002) J. Numer. Math. , vol.10 , pp. 249-274
    • Kanschat, G.1    Rannacher, R.2
  • 24
    • 11744250187 scopus 로고    scopus 로고
    • Block-triangular preconditioners for saddle point problems with a penalty term
    • A. KLAWONN, Block-triangular preconditioners for saddle point problems with a penalty term, SIAM J. Sci. Comput., 19 (1998), pp. 172-184.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 172-184
    • Klawonn, A.1
  • 25
    • 35048849954 scopus 로고    scopus 로고
    • Overlapping preconditioners for discontinuous Galerkin approximations of second order problems
    • N. Debit, M. Garbey, R. H. W. Hoppe, J. Périaux, D. Keyes, and Y. A. Kuznetsov, eds., DDM.org
    • C. LASSER AND A. TOSELLI, Overlapping preconditioners for discontinuous Galerkin approximations of second order problems, in Proceedings of the Thirteenth International Conference on Domain Decomposition Methods, N. Debit, M. Garbey, R. H. W. Hoppe, J. Périaux, D. Keyes, and Y. A. Kuznetsov, eds., DDM.org, 2001. Available online at http://ddm.org/DD13/homepage/
    • (2001) Proceedings of the Thirteenth International Conference on Domain Decomposition Methods
    • Lasser, C.1    Toselli, A.2
  • 26
    • 0034497397 scopus 로고    scopus 로고
    • A note on preconditioning for indefinite linear systems
    • M. F. MURPHY, G. H. GOLUB, AND A. J. WATHEN, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput., 21 (2000), pp. 1969-1972.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1969-1972
    • Murphy, M.F.1    Golub, G.H.2    Wathen, A.J.3
  • 28
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • M. F. WHEELER, An elliptic collocation-finite element method with interior penalties, SIAM J. Numer. Anal., 15 (1978), pp. 152-161.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.