메뉴 건너뛰기




Volumn 43, Issue 5, 2005, Pages 2012-2033

A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty

Author keywords

Convection diffusion problem; Crouzeix Raviart element; Finite element approximation; Interior penalty

Indexed keywords

DIFFUSION; GALERKIN METHODS; GRADIENT METHODS; PROBLEM SOLVING; THEOREM PROVING;

EID: 33745674971     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903437374     Document Type: Article
Times cited : (121)

References (27)
  • 1
    • 0038682938 scopus 로고    scopus 로고
    • A finite element method for domain decomposition with non-matching grids
    • R. BECKER, P. HANSBO, AND R. STENBERG, A finite element method for domain decomposition with non-matching grids, M2AN Math. Model. Numer. Anal., 37 (2003), pp. 209-225.
    • (2003) M2AN Math. Model. Numer. Anal. , vol.37 , pp. 209-225
    • Becker, R.1    Hansbo, P.2    Stenberg, R.3
  • 3
    • 0035621950 scopus 로고    scopus 로고
    • A minimal stabilisation procedure for mixed finite element methods
    • F. BREZZI AND M. FORTIN, A minimal stabilisation procedure for mixed finite element methods, Numer. Math., 89 (2001), pp. 457-491.
    • (2001) Numer. Math. , vol.89 , pp. 457-491
    • Brezzi, F.1    Fortin, M.2
  • 4
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A. N. BROOKS AND T. J. R. HUGHES, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 32 (1982), pp. 199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 5
    • 27144504688 scopus 로고    scopus 로고
    • Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence
    • E. BURMAN AND A. ERN, Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence, Math. Comp., 74 (2005), pp. 1637-1652.
    • (2005) Math. Comp. , vol.74 , pp. 1637-1652
    • Burman, E.1    Ern, A.2
  • 6
    • 2042428741 scopus 로고    scopus 로고
    • Edge stabilization for Galerkin approximations of convection-diffusion- reaction problems
    • E. BURMAN AND P. HANSBO, Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems, Comput. Methods Appl. Mech, Engrg., 193 (2004), pp. 1437-1453.
    • (2004) Comput. Methods Appl. Mech, Engrg. , vol.193 , pp. 1437-1453
    • Burman, E.1    Hansbo, P.2
  • 7
    • 33750182486 scopus 로고    scopus 로고
    • A stabilized non-conforming finite element method for incompressible flow
    • to appear
    • E. BURMAN AND P. HANSBO, A stabilized non-conforming finite element method for incompressible flow, Comput. Methods Appl. Mech. Engrg., (2004), to appear.
    • (2004) Comput. Methods Appl. Mech. Engrg.
    • Burman, E.1    Hansbo, P.2
  • 8
    • 33750160474 scopus 로고    scopus 로고
    • Iterative substructuring methods based on Nitsche's matching conditions for the solution of advection-diffusion problems using interior penalty stabilization
    • E. BURMAN AND P. ZUNINO, Iterative Substructuring Methods Based on Nitsche's Matching Conditions for the Solution of Advection-Diffusion Problems Using Interior Penalty Stabilization, IACS tech. report, 2005.
    • (2005) IACS Tech. Report
    • Burman, E.1    Zunino, P.2
  • 9
    • 0034351658 scopus 로고    scopus 로고
    • Stabilization of incompressibility and connection through orthogonal sub-scales in finite element methods
    • R. CODINA, Stabilization of incompressibility and connection through orthogonal sub-scales in finite element methods, Comput. Methods Appl. Mech. Engrg., 190 (2000), pp. 1579-1599.
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 1579-1599
    • Codina, R.1
  • 10
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Computing Methods in Applied Sciences, Second Internat. Symposium, Versailles, 1975, Springer-Verlag, Berlin
    • J. DOUGLAS, JR. AND T. DUPONT, Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences, Second Internat. Symposium, Versailles, 1975, Lecture Notes in Phys. 58, Springer-Verlag, Berlin, 1976, pp. 207-216.
    • (1976) Lecture Notes in Phys. , vol.58 , pp. 207-216
    • Douglas Jr., J.1    Dupont, T.2
  • 11
    • 0033264647 scopus 로고    scopus 로고
    • Stabilization of Galerkin approximations of transport equations by subgrid modeling
    • J.-L. GUERMOND, Stabilization of Galerkin approximations of transport equations by subgrid modeling, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 1293-1316.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , pp. 1293-1316
    • Guermond, J.-L.1
  • 12
    • 0039924017 scopus 로고    scopus 로고
    • Element-oriented and edge-oriented local error estimators for nonconforming finite element methods
    • R. H. W. HOPPE AND B. WOHLMUTH, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numer., 30 (1996), pp. 237-263.
    • (1996) RAIRO Modél. Math. Anal. Numer. , vol.30 , pp. 237-263
    • Hoppe, R.H.W.1    Wohlmuth, B.2
  • 13
    • 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
  • 14
    • 0032515223 scopus 로고    scopus 로고
    • A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems
    • V. JOHN, G. MATTHIES, F. SCHIEWECK. AND L. TOBISKA, A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 166 (1998), pp. 85-97.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.166 , pp. 85-97
    • John, V.1    Matthies, G.2    Schieweck, F.3    Tobiska, L.4
  • 15
    • 0031327621 scopus 로고    scopus 로고
    • Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems
    • V. JOHN, J. M. MAUBACH, AND L. TOBISKA, Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems, Numer. Math., 78 (1997), pp. 165-188.
    • (1997) Numer. Math. , vol.78 , pp. 165-188
    • John, V.1    Maubach, J.M.2    Tobiska, L.3
  • 17
    • 84966238599 scopus 로고
    • An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
    • C. JOHNSON AND J. PITKÄRANTA, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp., 46 (1986), pp. 1-26.
    • (1986) Math. Comp. , vol.46 , pp. 1-26
    • Johnson, C.1    Pitkäranta, J.2
  • 18
    • 84966258545 scopus 로고
    • Crosswind smear and pointwise errors in streamline diffusion finite element methods
    • C. JOHNSON, A. H. SCHATZ, AND L. B. WAHLBIN, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp., 49 (1987), pp. 25-38.
    • (1987) Math. Comp. , vol.49 , pp. 25-38
    • Johnson, C.1    Schatz, A.H.2    Wahlbin, L.B.3
  • 19
    • 0002763761 scopus 로고
    • On a finite element method for solving the neutron transport equation
    • (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974), Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York
    • P. LESAINT AND P.-A. RAVIART, On a finite element method for solving the neutron transport equation, in Mathematical Aspects of Finite Elements in Partial Differential Equations (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974), Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, pp. 89-123.
    • (1974) Mathematical Aspects of Finite Elements in Partial Differential Equations , pp. 89-123
    • Lesaint, P.1    Raviart, P.-A.2
  • 20
    • 0034957842 scopus 로고    scopus 로고
    • The streamline-diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffusion problems
    • G. MATTHIES AND L. TOBISKA, The streamline-diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffusion problems, Computing, 66 (2001), pp. 343-364.
    • (2001) Computing , vol.66 , pp. 343-364
    • Matthies, G.1    Tobiska, L.2
  • 22
    • 84951671794 scopus 로고
    • Über ein variationsprinzip zur lösung von Dirichlet-problemen bei verwendung von teilräumen, die keinen randbedingungen unterworfen sind
    • J. NITSCHE, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg, 36 (1971), pp. 9-15.
    • (1971) Abh. Math. Sem. Univ. Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.1
  • 23
    • 0040447052 scopus 로고
    • On a bpx-Preconditioner for p1 Elements
    • FSU Jena, Jena, Germany
    • P. OSWALD, On a bpx-Preconditioner for p1 Elements, Tech. report, FSU Jena, Jena, Germany, 1991.
    • (1991) Tech. Report
    • Oswald, P.1
  • 24
    • 0026106576 scopus 로고
    • A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation
    • T. E. PETERSON, A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation, SIAM J. Numer. Anal., 28 (1991), pp. 133-140.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 133-140
    • Peterson, T.E.1
  • 26
    • 0003345958 scopus 로고    scopus 로고
    • Galerkin finite element methods for parabolic problems
    • Springer-Verlag, Berlin
    • V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Springer Ser. Comput. Math. 25, Springer-Verlag, Berlin, 1997.
    • (1997) Springer Ser. Comput. Math. , vol.25
    • Thomée, V.1
  • 27
    • 0031542765 scopus 로고    scopus 로고
    • How accurate is the streamline diffusion finite element method?
    • G. ZHOU, How accurate is the streamline diffusion finite element method? Math. Comp., 66 (1997), pp. 31-44.
    • (1997) Math. Comp. , vol.66 , pp. 31-44
    • Zhou, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.