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Volumn 51, Issue 1, 2004, Pages 19-45

Mixed finite element approximation of incompressible MHD problems based on weighted regularization

Author keywords

Incompressible magneto hydrodynamics; Mixed methods; Weighted regularization

Indexed keywords

ALUMINUM; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ELECTROLYSIS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MAGNETIC FIELD EFFECTS; MAXWELL EQUATIONS; PROBLEM SOLVING;

EID: 4344637794     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.02.005     Document Type: Article
Times cited : (61)

References (28)
  • 1
    • 0030115145 scopus 로고    scopus 로고
    • Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier-Stokes equations
    • Armero F., Simo J.C. Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 131:1996;41-90.
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.131 , pp. 41-90
    • Armero, F.1    Simo, J.C.2
  • 2
    • 38849105167 scopus 로고    scopus 로고
    • Deal.II differential equations analysis library
    • IWR, Universität Heidelberg
    • W. Bangerth, R. Hartmann, G. Kanschat, deal.II differential equations analysis library, Technical Reference, IWR, Universität Heidelberg, http://www.dealii.org.
    • Technical Reference
    • Bangerth, W.1    Hartmann, R.2    Kanschat, G.3
  • 4
    • 0026171212 scopus 로고
    • Stability of higher-order Hood-Taylor methods
    • Brezzi F., Falk R.S. Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28:1991;581-590.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 581-590
    • Brezzi, F.1    Falk, R.S.2
  • 5
    • 0003312979 scopus 로고
    • Mixed and hybrid finite element methods
    • New York: Springer
    • Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. Springer Ser. Comput. Math. vol. 15:1991;Springer, New York.
    • (1991) Springer Ser. Comput. Math. , vol.15
    • Brezzi, F.1    Fortin, M.2
  • 6
    • 0034382191 scopus 로고    scopus 로고
    • Singularities of electromagnetic fields in polyhedral domains
    • Costabel M., Dauge M. Singularities of electromagnetic fields in polyhedral domains. Arch. Rat. Mech. Anal. 151:2000;221-276.
    • (2000) Arch. Rat. Mech. Anal. , vol.151 , pp. 221-276
    • Costabel, M.1    Dauge, M.2
  • 7
    • 0036912227 scopus 로고    scopus 로고
    • Weighted regularization of Maxwell equations in polyhedral domains
    • Costabel M., Dauge M. Weighted regularization of Maxwell equations in polyhedral domains. Numer. Math. 93:2002;239-277.
    • (2002) Numer. Math. , vol.93 , pp. 239-277
    • Costabel, M.1    Dauge, M.2
  • 8
    • 0003074690 scopus 로고
    • Elliptic boundary value problems in corner domains
    • Berlin: Springer
    • Dauge M. Elliptic Boundary Value Problems in Corner Domains. Lecture Notes in Math. vol. 1341:1988;Springer, Berlin.
    • (1988) Lecture Notes in Math. , vol.1341
    • Dauge, M.1
  • 9
    • 0002307515 scopus 로고
    • Stationary Stokes and Navier-Stokes systems on two- or three-dimensional domains with corners. Part I: Linearized equations
    • Dauge M. Stationary Stokes and Navier-Stokes systems on two- or three-dimensional domains with corners. Part I: Linearized equations. SIAM J. Math. Anal. 20:(1):1989;74-97.
    • (1989) SIAM J. Math. Anal. , vol.20 , Issue.1 , pp. 74-97
    • Dauge, M.1
  • 10
    • 0000893691 scopus 로고    scopus 로고
    • Iterative methods for problems in computational fluid dynamics
    • R.H. Chan, T.F. Chan, & G.H. Golub. Singapore: Springer
    • Elman H.E., Silvester D.J., Wathen A.J. Iterative methods for problems in computational fluid dynamics. Chan R.H., Chan T.F., Golub G.H. Iterative Methods in Scientific Computing. 1997;271-327 Springer, Singapore.
    • (1997) Iterative Methods in Scientific Computing , pp. 271-327
    • Elman, H.E.1    Silvester, D.J.2    Wathen, A.J.3
  • 11
    • 0036003235 scopus 로고    scopus 로고
    • Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
    • Elman H.E., Silvester D.J., Wathen A.J. Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations. Numer. Math. 90:2002;665-688.
    • (2002) Numer. Math. , vol.90 , pp. 665-688
    • Elman, H.E.1    Silvester, D.J.2    Wathen, A.J.3
  • 12
    • 0031533599 scopus 로고    scopus 로고
    • Magnetostatic and electrostatic problems in inhomogeneous anisotropic media with irregular boundary and mixed boundary conditions
    • Fernandes P., Gilardi G. Magnetostatic and electrostatic problems in inhomogeneous anisotropic media with irregular boundary and mixed boundary conditions. Math. Models Methods Appl. Sci. 7:1997;957-991.
    • (1997) Math. Models Methods Appl. Sci. , vol.7 , pp. 957-991
    • Fernandes, P.1    Gilardi, G.2
  • 13
    • 0034557275 scopus 로고    scopus 로고
    • A stabilized finite element method for the incompressible magnetohydrodynamic equations
    • Gerbeau J.-F. A stabilized finite element method for the incompressible magnetohydrodynamic equations. Numer. Math. 87:2000;83-111.
    • (2000) Numer. Math. , vol.87 , pp. 83-111
    • Gerbeau, J.-F.1
  • 15
    • 0003320921 scopus 로고
    • Elliptic problems in nonsmooth domains
    • Boston: Pitman
    • Grisvard P. Elliptic Problems in Nonsmooth Domains. Monographs Stud. in Math. vol. 24:1985;Pitman, Boston.
    • (1985) Monographs Stud. in Math. , vol.24
    • Grisvard, P.1
  • 16
    • 0036337414 scopus 로고    scopus 로고
    • Mixed finite element approximation of an MHD problem involving conducting and insulating regions: The 2D case
    • Guermond J.-L., Minev P. Mixed finite element approximation of an MHD problem involving conducting and insulating regions: The 2D case. Modél. Math. Numér. Anal. 36:2002;517-536.
    • (2002) Modél. Math. Numér. Anal. , vol.36 , pp. 517-536
    • Guermond, J.-L.1    Minev, P.2
  • 17
    • 0242308992 scopus 로고    scopus 로고
    • Mixed finite element approximation of an MHD problem involving conducting and insulating regions: The 3D case
    • Guermond J.-L., Minev P. Mixed finite element approximation of an MHD problem involving conducting and insulating regions: The 3D case. Numer. Methods Partial Differ. Equ. 19:2003;709-731.
    • (2003) Numer. Methods Partial Differ. Equ. , vol.19 , pp. 709-731
    • Guermond, J.-L.1    Minev, P.2
  • 18
    • 84966202677 scopus 로고
    • On the existence and uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics
    • Gunzburger M.D., Meir A.J., Peterson J.S. On the existence and uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics. Math. Comp. 56:1991;523-563.
    • (1991) Math. Comp. , vol.56 , pp. 523-563
    • Gunzburger, M.D.1    Meir, A.J.2    Peterson, J.S.3
  • 19
    • 0344032759 scopus 로고    scopus 로고
    • Analytic regularity of Stokes flow in polygonal domains
    • SAM, ETH Zürich, Zürich
    • B.Q. Guo, C. Schwab, Analytic regularity of Stokes flow in polygonal domains, Tech. Report 2000-18, SAM, ETH Zürich, Zürich, 2000.
    • (2000) Tech. Report , vol.2000 , Issue.18
    • Guo, B.Q.1    Schwab, C.2
  • 22
    • 0037791984 scopus 로고    scopus 로고
    • The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
    • Perugia I., Schötzau D. The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations. Math. Comp. 72:2003;1179-1214.
    • (2003) Math. Comp. , vol.72 , pp. 1179-1214
    • Perugia, I.1    Schötzau, D.2
  • 24
    • 0042205043 scopus 로고    scopus 로고
    • Mixed finite elements for incompressible magneto-hydrodynamics
    • Schneebeli A., Schötzau D. Mixed finite elements for incompressible magneto-hydrodynamics. C. R. Acad. Sci. Paris, Sér. I. 337:2003;71-74.
    • (2003) C. R. Acad. Sci. Paris, Sér. I , vol.337 , pp. 71-74
    • Schneebeli, A.1    Schötzau, D.2
  • 25
    • 12144290646 scopus 로고    scopus 로고
    • Mixed finite element methods for stationary incompressible magneto-hydrodynamics
    • Schötzau D. Mixed finite element methods for stationary incompressible magneto-hydrodynamics. Numer. Math. 96:2004;771-800.
    • (2004) Numer. Math. , vol.96 , pp. 771-800
    • Schötzau, D.1
  • 26
    • 0035529694 scopus 로고    scopus 로고
    • Exponential convergence in a Galerkin least squares hp -FEM for Stokes flow
    • Schötzau D., Schwab C. Exponential convergence in a Galerkin least squares hp -FEM for Stokes flow. IMA J. Numer. Anal. 2001;53-80.
    • (2001) IMA J. Numer. Anal. , pp. 53-80
    • Schötzau, D.1    Schwab, C.2
  • 28
    • 0005410031 scopus 로고    scopus 로고
    • Efficient solvers for incompressible flow problems
    • Berlin: Springer
    • Turek S. Efficient Solvers for Incompressible Flow Problems. Lecture Notes in Comput. Sci. Engrg. vol. 6:1999;Springer, Berlin.
    • (1999) Lecture Notes in Comput. Sci. Engrg. , vol.6
    • Turek, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.