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Volumn 35, Issue 2, 1998, Pages 712-727

An H1-galerkin mixed finite element method for parabolic partial differential equations

Author keywords

Backward Euler's method; Elliptic projection; Error estimates; Gronwall's lemma; H1 Galerkin; Lbb condition; Mixed finite element method; Parabolic initial and boundary value problem; Semidiscrete scheme

Indexed keywords


EID: 0039497039     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995280808     Document Type: Article
Times cited : (94)

References (31)
  • 1
    • 0003199785 scopus 로고
    • Mixed finite elements for second order elliptic problems in three variables
    • F. BREZZI, J. DOUGLAS, JR., R. DURÁN, AND M. FORTIN, Mixed finite elements for second order elliptic problems in three variables, Numer. Math., 51 (1987), pp. 237-250.
    • (1987) Numer. Math. , vol.51 , pp. 237-250
    • Brezzi, F.1    Douglas J., Jr.2    Durán, R.3    Fortin, M.4
  • 2
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • F. BREZZI, J. DOUGLAS, JR., AND L. D. MARINI, Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), pp. 217-235.
    • (1985) Numer. Math. , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas J., Jr.2    Marini, L.D.3
  • 4
    • 0024750086 scopus 로고
    • Convergence studies of least-square finite elements for first order systems
    • G. F. CAREY AND Y. SHEN, Convergence studies of least-square finite elements for first order systems, Comm. Appl. Numer. Methods, 5 (1989), pp. 427-434.
    • (1989) Comm. Appl. Numer. Methods , vol.5 , pp. 427-434
    • Carey, G.F.1    Shen, Y.2
  • 5
    • 0025496931 scopus 로고
    • A least-squares finite element method for the Helmholtz equation
    • C. L. CHANG, A least-squares finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 83 (1990), pp. 1-7.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.83 , pp. 1-7
    • Chang, C.L.1
  • 6
    • 84985305525 scopus 로고
    • On least-square approximations to compressible flow problems
    • T. F. CHEN, On least-square approximations to compressible flow problems, Numer. Methods Partial Differential Equations, 2 (1986), pp. 207-228.
    • (1986) Numer. Methods Partial Differential Equations , vol.2 , pp. 207-228
    • Chen, T.F.1
  • 7
    • 0026895693 scopus 로고
    • Error estimates for mixed finite element methods for nonlinear parabolic problems
    • S. H. CHOU AND Q. Li, Error estimates for mixed finite element methods for nonlinear parabolic problems, Numer. Methods Partial Differential Equations, 8 (1992), pp. 395-404.
    • (1992) Numer. Methods Partial Differential Equations , vol.8 , pp. 395-404
    • Chou, S.H.1    Li, Q.2
  • 8
    • 0025491777 scopus 로고
    • A priori estimates for mixed finite element methods for the wave equation
    • L. C. COWSAR, T. F. DUPONT, AND M. F. WHEELER, A priori estimates for mixed finite element methods for the wave equation, Comput. Methods Appl. Mech. Engrg., 82 (1990), pp. 205-222.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.82 , pp. 205-222
    • Cowsar, L.C.1    Dupont, T.F.2    Wheeler, M.F.3
  • 10
    • 0002329650 scopus 로고
    • Approximation of the pressure by a mixed method in the simulation of miscible displacement
    • J. DOUGLAS, JR., R. E. EWING, AND M. F. WHEELER, Approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numer., 17 (1983), pp. 17-33.
    • (1983) RAIRO Anal. Numer. , vol.17 , pp. 17-33
    • Douglas J., Jr.1    Ewing, R.E.2    Wheeler, M.F.3
  • 11
    • 84966242123 scopus 로고
    • Global estimates for mixed methods for the second order elliptic equations
    • J. DOUGLAS, JR., AND J. E. ROBERTS, Global estimates for mixed methods for the second order elliptic equations, Math. Comp., 44 (1985), pp. 39-52.
    • (1985) Math. Comp. , vol.44 , pp. 39-52
    • Douglas J., Jr.1    Roberts, J.E.2
  • 12
    • 0346904987 scopus 로고
    • On the approximation of miscible displacement in porous media by a method of characteristics combined with a mixed method
    • R. G. DURÁN. On the approximation of miscible displacement in porous media by a method of characteristics combined with a mixed method, SIAM J. Numer. Anal., 25 (1988), pp. 989-1001.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 989-1001
    • Durán, R.G.1
  • 13
    • 0021615427 scopus 로고
    • Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
    • R. E. EWING, T. F. RUSSEL, AND M. F. WHEELER, Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics, Comput. Methods Appl. Mech. Engrg., 47 (1984), pp. 73-92.
    • (1984) Comput. Methods Appl. Mech. Engrg. , vol.47 , pp. 73-92
    • Ewing, R.E.1    Russel, T.F.2    Wheeler, M.F.3
  • 14
    • 0006352903 scopus 로고
    • On the mixed finite element methods for first order elliptic systems
    • G. J. Fix, M. D. GUNZBURGER, AND R. A. NICOLAIDES, On the mixed finite element methods for first order elliptic systems. Numer. Math., 37 (1981), pp. 29-48.
    • (1981) Numer. Math. , vol.37 , pp. 29-48
    • Fix, G.J.1    Gunzburger, M.D.2    Nicolaides, R.A.3
  • 15
    • 0037736969 scopus 로고
    • On the application of mixed finite element methods to the wave equation
    • T. GEVECI, On the application of mixed finite element methods to the wave equation, Math. Model. Numer. Anal, 22 (1988), pp. 243-250.
    • (1988) Math. Model. Numer. Anal , vol.22 , pp. 243-250
    • Geveci, T.1
  • 16
    • 0021371362 scopus 로고
    • On different finite element methods for approximating the gradient of the solution to the Helmholtz equation
    • J. HASLINGER AND P. NEITTAANMÄKI, On different finite element methods for approximating the gradient of the solution to the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 42 (1984), pp. 131-148.
    • (1984) Comput. Methods Appl. Mech. Engrg. , vol.42 , pp. 131-148
    • Haslinger, J.1    Neittaanmäki, P.2
  • 17
    • 0002078165 scopus 로고
    • Error estimates for some mixed finite element methods for parabolic type problems
    • C. JOHNSON AND V. THOMÉE, Error estimates for some mixed finite element methods for parabolic type problems, RAIRO Numer. Anal., 15 (1981), pp. 41-78.
    • (1981) RAIRO Numer. Anal. , vol.15 , pp. 41-78
    • Johnson, C.1    Thomée, V.2
  • 18
    • 0039270843 scopus 로고
    • On finite element approximation of the gradient for solution of Poisson equations
    • P. NEITTAANMÄKI AND J. SARANEN, On finite element approximation of the gradient for solution of Poisson equations, Numer. Math., 37 (1981), pp. 333-337.
    • (1981) Numer. Math. , vol.37 , pp. 333-337
    • Neittaanmäki, P.1    Saranen, J.2
  • 19
    • 84979111684 scopus 로고
    • On the finite element approximation of vector fields by curl and divergence
    • P. NEITTAANMÄKI AND J. SARANEN, On the finite element approximation of vector fields by curl and divergence, Math. Methods Appl. Sci., 3 (1981), pp. 328-335.
    • (1981) Math. Methods Appl. Sci. , vol.3 , pp. 328-335
    • Neittaanmäki, P.1    Saranen, J.2
  • 20
    • 0019686346 scopus 로고
    • A mixed finite element method for the heat flow problem
    • P. NEITTAANMÄKI AND J. SARANEN, A mixed finite element method for the heat flow problem, BIT, 21 (1981), pp. 342-346.
    • (1981) BIT , vol.21 , pp. 342-346
    • Neittaanmäki, P.1    Saranen, J.2
  • 21
    • 0348060006 scopus 로고
    • Mixed Finite Element Method for a Stefan Problem
    • Department of Mathematics, IIT, Bombay
    • A. K. PANI, Mixed Finite Element Method for a Stefan Problem, Tech. report. Department of Mathematics, IIT, Bombay, 1988.
    • (1988) Tech. Report
    • Pani, A.K.1
  • 22
    • 0346799061 scopus 로고
    • 1-Galerkin method for quasilinear parabolic partial differential equations
    • C. A. Micchelli, D. V. Pai, and B. V. Limaye, eds., ISNM 76, Birkhäuser-Verlag, Basel
    • 1-Galerkin method for quasilinear parabolic partial differential equations, Methods of Functional Analysis in Approximation Theory, C. A. Micchelli, D. V. Pai, and B. V. Limaye, eds., ISNM 76, Birkhäuser-Verlag, Basel, 1986, pp. 357-370.
    • (1986) Methods of Functional Analysis in Approximation Theory , pp. 357-370
    • Pani, A.K.1    Das, P.C.2
  • 23
    • 0348060005 scopus 로고
    • Finite element methods for identification of parameters in parabolic problems
    • A. K. Pani and R. S. Anderssen, eds., Australian National University, Canberra
    • A. K. PANI AND R. S. ANDERSSEN, Finite element methods for identification of parameters in parabolic problems. Inverse Problems in Partial Differential Equations, Proc. Centre for Mathematics and Its Applications, Vol. 31, A. K. Pani and R. S. Anderssen, eds., Australian National University, Canberra, 1992, pp. 208-221.
    • (1992) Inverse Problems in Partial Differential Equations, Proc. Centre for Mathematics and Its Applications , vol.31 , pp. 208-221
    • Pani, A.K.1    Anderssen, R.S.2
  • 24
    • 0001492022 scopus 로고
    • Convergence analysis of least-square mixed finite elements
    • A. I. PEHLIVANOV, G. F. CAREY, R. D. LAZAROV, AND Y. SHEN, Convergence analysis of least-square mixed finite elements, Computing, 51 (1993), pp. 111-123.
    • (1993) Computing , vol.51 , pp. 111-123
    • Pehlivanov, A.I.1    Carey, G.F.2    Lazarov, R.D.3    Shen, Y.4
  • 25
    • 0028517692 scopus 로고
    • Least-square mixed finite elements for second order elliptic problems
    • A. I. PEHLIVANOV, G. F. CAREY, AND R. D. LAZAROV, Least-square mixed finite elements for second order elliptic problems. SIAM J. Numer. Anal., 31 (1994), pp. 1368-1377.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1368-1377
    • Pehlivanov, A.I.1    Carey, G.F.2    Lazarov, R.D.3
  • 27
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Springer-Verlag, New York
    • P. A. RAVIART AND J. M. THOMAS, A mixed finite element method for second order elliptic problems, Lecture Notes in Mathematics 606, Springer-Verlag, New York, 1977, pp. 293-315.
    • (1977) Lecture Notes in Mathematics , vol.606 , pp. 293-315
    • Raviart, P.A.1    Thomas, J.M.2
  • 28
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • R.E. Ewing, ed., SIAM, Phildelphia
    • T. F. RUSSEL AND M. F. WHEELER, Finite element and finite difference methods for continuous flows in porous media, The Mathematics of Reservoir Simulation, R.E. Ewing, ed., SIAM, Phildelphia, 1983, pp. 35-106.
    • (1983) The Mathematics of Reservoir Simulation , pp. 35-106
    • Russel, T.F.1    Wheeler, M.F.2
  • 29
    • 0003208045 scopus 로고
    • Galerkin finite element methods for parabolic problems
    • Springer-Verlag. New York
    • V. THOMÉE, Galerkin finite element methods for parabolic problems, Lecture Notes in Mathematics 1054, Springer-Verlag. New York, 1984.
    • (1984) Lecture Notes in Mathematics , vol.1054
    • Thomée, V.1
  • 30
    • 0016519316 scopus 로고
    • On Galerkin methods in semilinear parabolic problems
    • V. THOMÉE AND L. B. WAHLBIN, On Galerkin methods in semilinear parabolic problems, SIAM J. Numer. Anal., 12 (1989), pp. 376-389.
    • (1989) SIAM J. Numer. Anal. , vol.12 , pp. 376-389
    • Thomée, V.1    Wahlbin, L.B.2
  • 31
    • 0001287713 scopus 로고
    • 2-error estimates for Galerkin approximations to parabolic differential equations
    • 2-error estimates for Galerkin approximations to parabolic differential equations, SIAM J. Numer. Anal., 10 (1973), pp. 723-749.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 723-749
    • Wheeler, M.F.1


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