메뉴 건너뛰기




Volumn 40, Issue 6, 2002, Pages 2171-2194

Mixed hp-DGFEM for incompressible flows

Author keywords

Discontinuous Galerkin methods; hp FEM; Stokes problem

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; DIFFUSION; ERROR ANALYSIS; FINITE ELEMENT METHOD; FUNCTIONS; GALERKIN METHODS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; POLYNOMIALS; TENSORS; THEOREM PROVING;

EID: 0345708744     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901399124     Document Type: Article
Times cited : (155)

References (41)
  • 1
    • 0141962816 scopus 로고    scopus 로고
    • hp-approximation theory for BDFM and RT finite elements on quadrilaterals
    • M. AINSWORTH AND K. PINCHEDEZ, hp-approximation theory for BDFM and RT finite elements on quadrilaterals, SIAM J. Numer. Anal., 40 (2002), pp. 2047-2068.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 2047-2068
    • Ainsworth, M.1    Pinchedez, K.2
  • 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. MARTNI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779.
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Martni, L.D.4
  • 3
    • 0000026672 scopus 로고
    • The hp-version of the finite element method with quasiuniform meshes
    • I. BABUŠKA AND M. SURI, The hp-version of the finite element method with quasiuniform meshes, RAIRO Anal. Numér., 21 (1987), pp. 199-238.
    • (1987) RAIRO Anal. Numér. , vol.21 , pp. 199-238
    • Babuška, I.1    Suri, M.2
  • 4
    • 0000812911 scopus 로고
    • Piecewise solenoidal vector fields and the Stokes problem
    • G.A. BAKER, W.N. JUREIDINI, AND O.A. KARAKASHIAN, Piecewise solenoidal vector fields and the Stokes problem, SIAM J. Numer. Anal., 27 (1990), pp. 1466-1485.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1466-1485
    • Baker, G.A.1    Jureidini, W.N.2    Karakashian, O.A.3
  • 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
  • 7
    • 0345062335 scopus 로고    scopus 로고
    • A discontinuous hp-finite element method for convection-diffusion problems
    • C.E. BAUMANN AND J.T. ODEN, A discontinuous hp-finite element method for convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 311-341.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.175 , pp. 311-341
    • Baumann, C.E.1    Oden, J.T.2
  • 8
    • 0003170104 scopus 로고
    • Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes
    • Vieweg, Braunschweig, Germany
    • R. BECKER AND R. RANNACHER, Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes, in Proceedings of the 10th GAMM Seminar, Notes Numer. Fluid Dynamics, Vieweg, Braunschweig, Germany, 1995, pp. 52-62.
    • (1995) Proceedings of the 10th GAMM Seminar, Notes Numer. Fluid Dynamics , pp. 52-62
    • Becker, R.1    Rannacher, R.2
  • 9
    • 67349095304 scopus 로고    scopus 로고
    • Spectral methods
    • North-Holland, Amsterdam
    • C. BERNARDI AND Y. MADAY, Spectral methods, in Handbook of Numerical Analysis 5, North-Holland, Amsterdam, 1997, pp. 209-485.
    • (1997) Handbook of Numerical Analysis , vol.5 , pp. 209-485
    • Bernardi, C.1    Maday, Y.2
  • 10
    • 0003312979 scopus 로고
    • Mixed and Hybrid Finite Element Methods
    • Springer-Verlag, New York
    • F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer Ser. Comput. Math. 15, Springer-Verlag, New York, 1991.
    • (1991) Springer Ser. Comput. Math. , vol.15
    • Brezzi, F.1    Fortin, M.2
  • 12
    • 84968491212 scopus 로고
    • Approximation results for orthogonal polynomials in Sobolev spaces
    • C. CANUTO AND A. QUARTERONI, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38 (1982), pp. 67-86.
    • (1982) Math. Comp. , vol.38 , pp. 67-86
    • Canuto, C.1    Quarteroni, A.2
  • 13
    • 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
  • 14
    • 0036013520 scopus 로고    scopus 로고
    • Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems
    • P. CASTILLO, B. COCKBURN, D. SCHÖTZAU, AND C. SCHWAB, Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems, Math. Comp., 71 (2002), pp. 455-478.
    • (2002) Math. Comp. , vol.71 , pp. 455-478
    • Castillo, P.1    Cockburn, B.2    Schötzau, D.3    Schwab, C.4
  • 15
    • 0002718851 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for convection-dominated problems
    • T. Barth and H. Deconink, eds., Springer-Verlag, Berlin
    • B. COCKBURN, Discontinuous Galerkin methods for convection-dominated problems, in High-Order Methods for Computational Physics, T. Barth and H. Deconink, eds., Springer-Verlag, Berlin, 1999, pp. 69-224.
    • (1999) High-order Methods for Computational Physics , pp. 69-224
    • Cockburn, B.1
  • 18
    • 0002718853 scopus 로고    scopus 로고
    • Discontinuous Galerkin Methods. Theory, Computation and Applications
    • Springer-Verlag, Berlin
    • B. COCKBURN, G.E. KARNIADAKIS, AND C.-W. SHU, EDS., Discontinuous Galerkin Methods. Theory, Computation and Applications, Lect. Notes Comput. Sci. Eng. 11, Springer-Verlag, Berlin, 2000.
    • (2000) Lect. Notes Comput. Sci. Eng. , vol.11
    • Cockburn, B.1    Karniadakis, G.E.2    Shu, C.-W.3
  • 19
    • 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
  • 20
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • B. COCKBURN AND C.-W. SHU, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput., 16 (2001), pp. 173-261.
    • (2001) J. Sci. Comput. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 21
    • 0026928030 scopus 로고
    • Stabilized finite element methods, II. The incompressible Navier-Stokes equations
    • L. FRANCA AND S. L. FREY, Stabilized finite element methods, II. The incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 99 (1992), pp. 209-233.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.99 , pp. 209-233
    • Franca, L.1    Frey, S.L.2
  • 22
    • 0026386228 scopus 로고
    • Error analysis of some Galerkin least squares methods for the elasticity equations
    • L. P. FRANCA AND R. STENBERG, Error analysis of some Galerkin least squares methods for the elasticity equations, SIAM J. Numer. Anal., 28 (1991), pp. 1680-1697.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1680-1697
    • Franca, L.P.1    Stenberg, R.2
  • 23
    • 0038077133 scopus 로고    scopus 로고
    • hp-DGFEM on Shape-Irregular Meshes: Reaction-Diffusion
    • Oxford University Computing Laboratory, Oxford University, Oxford
    • E.H. GEORGOULIS AND E. SÜLI, hp-DGFEM on Shape-Irregular Meshes: Reaction-Diffusion, Technical report NA 01-09, Oxford University Computing Laboratory, Oxford University, Oxford, 2001.
    • (2001) Technical Report , vol.NA 01-09
    • Georgoulis, E.H.1    Süli, E.2
  • 24
    • 0001521891 scopus 로고    scopus 로고
    • Stabilized spectral element approximation for the Navier-Stokes equations
    • P. GERVASIO AND F. SALERI, Stabilized spectral element approximation for the Navier-Stokes equations, Numer. Methods Partial Differential Equations, 14 (1998), pp. 115-141.
    • (1998) Numer. Methods Partial Differential Equations , vol.14 , pp. 115-141
    • Gervasio, P.1    Saleri, F.2
  • 26
    • 0037085994 scopus 로고    scopus 로고
    • Discontinuous finite element methods for incompressible and nearly incompressible elasticity by use of Nitsche's method
    • P. HANSBO AND M.G. LARSON, Discontinuous finite element methods for incompressible and nearly incompressible elasticity by use of Nitsche's method, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 1895-1908.
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 1895-1908
    • Hansbo, P.1    Larson, M.G.2
  • 27
    • 0036556363 scopus 로고    scopus 로고
    • Discontinuous hp-finite element methods for advection-diffusion-reaction problems
    • P. HOUSTON, C. SCHWAB, AND E. SÜLI, Discontinuous hp-finite element methods for advection-diffusion-reaction problems, SIAM J. Numer. Anal., 39 (2002), pp. 2133-2163.
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 2133-2163
    • Houston, P.1    Schwab, C.2    Süli, E.3
  • 28
    • 0001408252 scopus 로고    scopus 로고
    • A nonconforming finite element method for the stationary Navier-Stokes equations
    • O.A. KARAKASHIAN AND W.N. JUREIDINI, A nonconforming finite element method for the stationary Navier-Stokes equations, SIAM J. Numer. Anal., 35 (1998), pp. 93-120.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 93-120
    • Karakashian, O.A.1    Jureidini, W.N.2
  • 29
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp-finite element method for diffusion problems
    • J.T. ODEN, I. BABUŠHKA, AND C.E. BAUMANN, A discontinuous hp-finite element method for diffusion problems, J. Comput. Phys., 146 (1998), pp. 491-519.
    • (1998) J. Comput. Phys. , vol.146 , pp. 491-519
    • Oden, J.T.1    Babušhka, I.2    Baumann, C.E.3
  • 30
    • 0347522228 scopus 로고    scopus 로고
    • The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell's equations
    • to appear
    • I. PERUGIA AND D. SCHÖTZAU, The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell's equations, Math. Comp., to appear.
    • Math. Comp.
    • Perugia, I.1    Schötzau, D.2
  • 31
    • 0348152044 scopus 로고    scopus 로고
    • An hp-analysis of the local discontinuous Galerkin method for diffusion problems
    • I. PERUGIA AND D. SCHÖTZAU, An hp-analysis of the local discontinuous Galerkin method for diffusion problems, J. Sci. Comput., 17 (2002), pp. 561-571.
    • (2002) J. Sci. Comput. , vol.17 , pp. 561-571
    • Perugia, I.1    Schötzau, D.2
  • 32
    • 0010974891 scopus 로고    scopus 로고
    • Review of A Priori Error Estimation for Discontinuous Galerkin Methods
    • TICAM, University of Texas at Austin, Austin, Texas
    • S. PRUDHOMME, F. PASCAL, J.T. ODEN, AND A. ROMKES, Review of A Priori Error Estimation for Discontinuous Galerkin Methods, Technical report 2000-27, TICAM, University of Texas at Austin, Austin, Texas, 2000.
    • (2000) Technical Report , vol.2000 , Issue.27
    • Prudhomme, S.1    Pascal, F.2    Oden, J.T.3    Romkes, A.4
  • 35
    • 0033511173 scopus 로고    scopus 로고
    • Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems, Part I
    • B. RIVIÈRE, M.F. WHEELER, AND V. GIRAULT, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems, Part I, Computational Geosciences, 3 (1999), pp. 337-360.
    • (1999) Computational Geosciences , vol.3 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 36
    • 0040714266 scopus 로고    scopus 로고
    • Mixed hp-FEM on anisotropic meshes, II. Hanging nodes and tensor products of boundary layer meshes
    • D. SCHÖTZAU, C. SCHWAB, AND R. STENBERG, Mixed hp-FEM on anisotropic meshes, II. Hanging nodes and tensor products of boundary layer meshes, Numer. Math., 83 (1999), pp. 667-697.
    • (1999) Numer. Math. , vol.83 , pp. 667-697
    • Schötzau, D.1    Schwab, C.2    Stenberg, R.3
  • 38
    • 0039270320 scopus 로고    scopus 로고
    • Mixed hp-finite element methods for problems in elasticity and Stokes flow
    • R. STENBERG AND M. SURI, Mixed hp-finite element methods for problems in elasticity and Stokes flow, Numer. Math., 72 (1996), pp. 367-389.
    • (1996) Numer. Math. , vol.72 , pp. 367-389
    • Stenberg, R.1    Suri, M.2
  • 40
    • 0036857697 scopus 로고    scopus 로고
    • hp-discontinuous Galerkin approximations for the Stokes problem
    • A. TOSELLI, hp-discontinuous Galerkin approximations for the Stokes problem, Math. Models Methods Appl. Sci., 12 (2002), pp. 1565-1616.
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , pp. 1565-1616
    • Toselli, A.1
  • 41
    • 0012742868 scopus 로고    scopus 로고
    • Mixed hp-Finite Element Approximations on Geometric Edge and Boundary Layer Meshes in Three Dimensions
    • Seminar for Applied Mathematics, ETHZ, Zürich, Switzerland, Numer. Math., to appear
    • A. TOSELLI AND C. SCHWAB, Mixed hp-Finite Element Approximations on Geometric Edge and Boundary Layer Meshes in Three Dimensions, Technical report 2001-02, Seminar for Applied Mathematics, ETHZ, Zürich, Switzerland, 2001; Numer. Math., to appear.
    • (2001) Technical Report , vol.2001-2002
    • Toselli, A.1    Schwab, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.