메뉴 건너뛰기




Volumn 199, Issue 41-44, 2010, Pages 2709-2720

A conservative and monotone mixed-hybridized finite element approximation of transport problems in heterogeneous domains

Author keywords

Electrophysiology; Heterogeneous problems; Mathematical modeling; Mixed hybridized finite element methods; Neuroelectronics; Numerical simulation; Transport phenomena

Indexed keywords

FINITE ELEMENT; HETEROGENEOUS PROBLEMS; MATHEMATICAL MODELING; NEUROELECTRONICS; NUMERICAL SIMULATION; TRANSPORT PHENOMENA;

EID: 77957599840     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.05.016     Document Type: Article
Times cited : (18)

References (64)
  • 1
    • 33645637527 scopus 로고    scopus 로고
    • Computational Cell Biology
    • Springer, New York, (Corr. 3rd printing, 2004), C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson (Eds.)
    • Computational Cell Biology. Interdisciplinary Applied Mathematics 2002, vol. 20. Springer, New York, (Corr. 3rd printing, 2004). 1st ed. C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson (Eds.).
    • (2002) Interdisciplinary Applied Mathematics , vol.20
  • 2
    • 85097981054 scopus 로고    scopus 로고
    • Microflows and Nanoflows. Fundamentals and Simulation
    • Springer, New York, G.E. Karniadakis, A. Beskok, N. Aluru (Eds.)
    • Microflows and Nanoflows. Fundamentals and Simulation. Interdisciplinary Applied Mathematics 2005, vol. 29. Springer, New York. G.E. Karniadakis, A. Beskok, N. Aluru (Eds.).
    • (2005) Interdisciplinary Applied Mathematics , vol.29
  • 3
    • 0029505980 scopus 로고
    • Connection between finite volume and mixed finite element methods for a diffusion problem with nonconstant coefficients application to a convection-diffusion problem
    • Agouzal A., Baranger J., Maitre J.F., Oudin F. Connection between finite volume and mixed finite element methods for a diffusion problem with nonconstant coefficients application to a convection-diffusion problem. East-West J. Numer. Math. 1995, 34:237-254.
    • (1995) East-West J. Numer. Math. , vol.34 , pp. 237-254
    • Agouzal, A.1    Baranger, J.2    Maitre, J.F.3    Oudin, F.4
  • 4
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates
    • Arnold D.N., Brezzi F. Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. Math. Model. Numer. Anal. 1985, 19-1:7-32.
    • (1985) Math. Model. Numer. Anal. , vol.1-19 , pp. 7-32
    • Arnold, D.N.1    Brezzi, F.2
  • 5
    • 0000828256 scopus 로고
    • Generalized finite element methods, their performance and their relation to mixed methods
    • Babuska I., Osborn J. Generalized finite element methods, their performance and their relation to mixed methods. SIAM J. Numer. Anal. 1983, 20:510-536.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 510-536
    • Babuska, I.1    Osborn, J.2
  • 7
    • 0001626911 scopus 로고
    • Some upwinding techniques for finite element approximations of convection-diffusion equations
    • Bank R.E., Burgler J.F., Fichtner W., Smith R.K. Some upwinding techniques for finite element approximations of convection-diffusion equations. Numer. Math. 1990, 58:185-202.
    • (1990) Numer. Math. , vol.58 , pp. 185-202
    • Bank, R.E.1    Burgler, J.F.2    Fichtner, W.3    Smith, R.K.4
  • 8
    • 0039989084 scopus 로고    scopus 로고
    • The finite volume Scharfetter-Gummel method for steady convection-diffusion equations
    • Bank R.E., Coughran W.M., Cowsar L.C. The finite volume Scharfetter-Gummel method for steady convection-diffusion equations. Comput. Visual. Sci. 1998, 1(3):123-136.
    • (1998) Comput. Visual. Sci. , vol.1 , Issue.3 , pp. 123-136
    • Bank, R.E.1    Coughran, W.M.2    Cowsar, L.C.3
  • 9
    • 0023401301 scopus 로고
    • Some error estimates for the box method
    • Bank R.E., Rose D.J. Some error estimates for the box method. SIAM J. Numer. Anal. 1987, 24(4):777-787.
    • (1987) SIAM J. Numer. Anal. , vol.24 , Issue.4 , pp. 777-787
    • Bank, R.E.1    Rose, D.J.2
  • 12
    • 77957559443 scopus 로고    scopus 로고
    • Multiphysics/Multiscale Computational Modeling in Neuroelectronics, Master Thesis, Politecnico di Milano, 2009.
    • M. Brera, Multiphysics/Multiscale Computational Modeling in Neuroelectronics, Master Thesis, Politecnico di Milano, 2009. http://www1.mate.polimi.it/biblioteca/tesvview.php?id=66&L=i.
    • Brera, M.1
  • 15
    • 33745962136 scopus 로고    scopus 로고
    • Stability and error analysis of mixed finite volume methods for advective-diffusive problems
    • Brezzi F., Marini L.D., Micheletti S., Pietra P., Sacco R. Stability and error analysis of mixed finite volume methods for advective-diffusive problems. Comput. Math. Appl. 2006, 51:681-696.
    • (2006) Comput. Math. Appl. , vol.51 , pp. 681-696
    • Brezzi, F.1    Marini, L.D.2    Micheletti, S.3    Pietra, P.4    Sacco, R.5
  • 17
    • 0001565447 scopus 로고
    • Méthodes d'éléments finis mixtes et schéma de Scharfetter-Gummel
    • Brezzi F., Marini L.D., Pietra P. Méthodes d'éléments finis mixtes et schéma de Scharfetter-Gummel. C.R. Acad. Sci., Paris 1987, 305(1):599-604.
    • (1987) C.R. Acad. Sci., Paris , vol.305 , Issue.1 , pp. 599-604
    • Brezzi, F.1    Marini, L.D.2    Pietra, P.3
  • 19
    • 0000617339 scopus 로고
    • Two-dimensional exponential fitting and applications to drift-diffusion models
    • Brezzi F., Marini L.D., Pietra P. Two-dimensional exponential fitting and applications to drift-diffusion models. SIAM J. Numer. Anal. 1989, 26:1342-1355.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1342-1355
    • Brezzi, F.1    Marini, L.D.2    Pietra, P.3
  • 20
    • 21644433886 scopus 로고    scopus 로고
    • Field-effect transistor with recombinant potassium channels: fast and slow response by electrical and chemical interactions
    • Brittinger M., Fromherz P. Field-effect transistor with recombinant potassium channels: fast and slow response by electrical and chemical interactions. Appl. Phys. A 2005, 81:439-447.
    • (2005) Appl. Phys. A , vol.81 , pp. 439-447
    • Brittinger, M.1    Fromherz, P.2
  • 21
    • 0019607241 scopus 로고
    • Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • Brooks A.N., Hughes T.J.R. Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 1982, 32:199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 22
    • 57049094391 scopus 로고    scopus 로고
    • A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
    • Cockburn B., Dong B., Guzmán J. A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems. Math. Comput. 2008, 77:1887-1916.
    • (2008) Math. Comput. , vol.77 , pp. 1887-1916
    • Cockburn, B.1    Dong, B.2    Guzmán, J.3
  • 23
    • 77957021648 scopus 로고    scopus 로고
    • An hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems
    • Cockburn B., Dong B., Guzman J., Restelli M., Sacco R. An hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. SIAM J. Sci. Comput. 2009, 31(5):3827-3846.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.5 , pp. 3827-3846
    • Cockburn, B.1    Dong, B.2    Guzman, J.3    Restelli, M.4    Sacco, R.5
  • 24
    • 20144361830 scopus 로고    scopus 로고
    • A characterization of hybridized mixed methods for second order elliptic problems
    • Cockburn B., Gopalakrishnan J. A characterization of hybridized mixed methods for second order elliptic problems. SIAM J. Numer. Anal. 2004, 42:283-301.
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 283-301
    • Cockburn, B.1    Gopalakrishnan, J.2
  • 25
    • 27144538207 scopus 로고    scopus 로고
    • Error analysis of variable degree mixed methods for elliptic problems via hybridization
    • Cockburn B., Gopalakrishnan J. Error analysis of variable degree mixed methods for elliptic problems via hybridization. Math. Comput. 2005, 74:1653-1677.
    • (2005) Math. Comput. , vol.74 , pp. 1653-1677
    • Cockburn, B.1    Gopalakrishnan, J.2
  • 26
    • 70349733642 scopus 로고    scopus 로고
    • Unified hybridization of discontinuous Galerkin mixed and continuous Galerkin methods for second order elliptic problems
    • Cockburn B., Gopalakrishnan J., Lazarov R. Unified hybridization of discontinuous Galerkin mixed and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 2009, 47:1319-1365.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 1319-1365
    • Cockburn, B.1    Gopalakrishnan, J.2    Lazarov, R.3
  • 27
    • 58149269239 scopus 로고    scopus 로고
    • Superconvergent discontinuous Galerkin methods for second-order elliptic problems
    • Cockburn B., Guzmán J., Wang H. Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Math. Comput. 2009, 78:1-24.
    • (2009) Math. Comput. , vol.78 , pp. 1-24
    • Cockburn, B.1    Guzmán, J.2    Wang, H.3
  • 28
    • 0015762231 scopus 로고
    • Conforming and non-conforming finite element methods for solving the stationary Stokes equations
    • Crouzeix M., Raviart P.A. Conforming and non-conforming finite element methods for solving the stationary Stokes equations. R.A.I.R.O. 1973, R-3:33-76.
    • (1973) R.A.I.R.O. , vol.3 R , pp. 33-76
    • Crouzeix, M.1    Raviart, P.A.2
  • 29
    • 77952544959 scopus 로고    scopus 로고
    • Analytical and numerical study of photocurrent transients in organic polymer solar cells
    • de Falco C., Sacco R., Verri M. Analytical and numerical study of photocurrent transients in organic polymer solar cells. Comput. Methods Appl. Mech. Engrg. 2010, 199:1722-1732.
    • (2010) Comput. Methods Appl. Mech. Engrg. , vol.199 , pp. 1722-1732
    • de Falco, C.1    Sacco, R.2    Verri, M.3
  • 30
    • 0001533213 scopus 로고
    • Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder
    • de D.N., Allen G., Southwell R.V. Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl. Math. 1955, 8:129-145.
    • (1955) Quart. J. Mech. Appl. Math. , vol.8 , pp. 129-145
    • de, D.N.1    Allen, G.2    Southwell, R.V.3
  • 31
    • 0001571646 scopus 로고
    • Sur la sphère vide. Izv. Akad. Nauk. SSSR
    • Delaunay B. Sur la sphère vide. Izv. Akad. Nauk. SSSR. Math. Nat. Sci. Div. 1934, 6:793-800.
    • (1934) Math. Nat. Sci. Div. , vol.6 , pp. 793-800
    • Delaunay, B.1
  • 33
    • 1442298511 scopus 로고    scopus 로고
    • Neuroelectronics interfacing: semiconductor chips with ion channels nerve, cells and brain
    • Wiley-VCH, Berlin, R. Weise (Ed.)
    • Fromherz P. Neuroelectronics interfacing: semiconductor chips with ion channels nerve, cells and brain. Nanoelectronics and Information Technology 2003, 781-810. Wiley-VCH, Berlin. R. Weise (Ed.).
    • (2003) Nanoelectronics and Information Technology , pp. 781-810
    • Fromherz, P.1
  • 34
    • 0031635793 scopus 로고    scopus 로고
    • A new Galerkin framework for the drift-diffusion equation in semiconductors
    • Gatti E., Micheletti S., Sacco R. A new Galerkin framework for the drift-diffusion equation in semiconductors. East-West J. Numer. Math. 1998, 6(2):101-135.
    • (1998) East-West J. Numer. Math. , vol.6 , Issue.2 , pp. 101-135
    • Gatti, E.1    Micheletti, S.2    Sacco, R.3
  • 36
    • 77956707015 scopus 로고
    • Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo
    • Hodgkin A.L., Huxley A.F. Currents carried by sodium and potassium ions through the membrane of the giant axon of loligo. J. Physiol. 1952, 116:449-472.
    • (1952) J. Physiol. , vol.116 , pp. 449-472
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 38
    • 0036435210 scopus 로고    scopus 로고
    • Analytical approaches to charge transport in a moving medium
    • Jerome J.W. Analytical approaches to charge transport in a moving medium. Transport Theo. Statist. Phys. 2002, 31:333-366.
    • (2002) Transport Theo. Statist. Phys. , vol.31 , pp. 333-366
    • Jerome, J.W.1
  • 39
    • 72149102698 scopus 로고    scopus 로고
    • Global weak solutions for an incompressible charged fluid with multi-scale couplings: initial-boundary value problem
    • Jerome J.W., Sacco R. Global weak solutions for an incompressible charged fluid with multi-scale couplings: initial-boundary value problem. Nonlinear Anal. 2009, 71:e2487-e2497.
    • (2009) Nonlinear Anal. , vol.71
    • Jerome, J.W.1    Sacco, R.2
  • 40
    • 42549123755 scopus 로고    scopus 로고
    • Computational modeling and simulation of complex systems in bio-electronics
    • Jerome J.W., Sacco R., Chini B., Longaretti M. Computational modeling and simulation of complex systems in bio-electronics. J. Comput. Electron. 2008, 7(1):10-13.
    • (2008) J. Comput. Electron. , vol.7 , Issue.1 , pp. 10-13
    • Jerome, J.W.1    Sacco, R.2    Chini, B.3    Longaretti, M.4
  • 42
    • 0008024913 scopus 로고    scopus 로고
    • Piecewise linear Petrov-Galerkin error estimates for the box method
    • Kerkhoven T. Piecewise linear Petrov-Galerkin error estimates for the box method. SIAM J. Numer. Anal. 1996, 33(5):1864-1884.
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.5 , pp. 1864-1884
    • Kerkhoven, T.1
  • 44
    • 42549155863 scopus 로고    scopus 로고
    • Computational modeling in nano-bio-electronics: simulation of ionic transport in voltage operated channels
    • Longaretti M., Marino G., Chini B., Jerome J.W., Sacco R. Computational modeling in nano-bio-electronics: simulation of ionic transport in voltage operated channels. J. Nanosci. Nanotechnol. 2007, 8:1-9.
    • (2007) J. Nanosci. Nanotechnol. , vol.8 , pp. 1-9
    • Longaretti, M.1    Marino, G.2    Chini, B.3    Jerome, J.W.4    Sacco, R.5
  • 45
    • 0001602095 scopus 로고
    • An abstract theory for mixed approximations of second order elliptic problems
    • Marini L.D., Pietra P. An abstract theory for mixed approximations of second order elliptic problems. Math. Appl. Comput. 1990, 8:219-239.
    • (1990) Math. Appl. Comput. , vol.8 , pp. 219-239
    • Marini, L.D.1    Pietra, P.2
  • 46
    • 0036208212 scopus 로고    scopus 로고
    • On some mixed finite element methods with numerical integration
    • Micheletti S., Sacco R., Saleri F. On some mixed finite element methods with numerical integration. SIAM J. Sci. Comput. 2001, 23-1:245-270.
    • (2001) SIAM J. Sci. Comput. , vol.1-23 , pp. 245-270
    • Micheletti, S.1    Sacco, R.2    Saleri, F.3
  • 47
    • 0037919204 scopus 로고
    • An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
    • 2AN 1994, 28(2):123-140.
    • (1994) 2AN , vol.28 , Issue.2 , pp. 123-140
    • Miller, J.J.1    Wang, S.2
  • 48
    • 77957217526 scopus 로고
    • A new non-conforming Petrov-Galerkin finite element method with triangular elements for an advection-diffusion problem
    • Miller J.J., Wang S. A new non-conforming Petrov-Galerkin finite element method with triangular elements for an advection-diffusion problem. IMA J. Numer. Anal. 1994, 14:257-276.
    • (1994) IMA J. Numer. Anal. , vol.14 , pp. 257-276
    • Miller, J.J.1    Wang, S.2
  • 49
    • 0028377559 scopus 로고
    • A tetrahedral mixed finite element method for the stationary semiconductor continuity equations
    • Miller J.J., Wang S. A tetrahedral mixed finite element method for the stationary semiconductor continuity equations. SIAM J. Numer. Anal. 1994, 31(1):196-216.
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.1 , pp. 196-216
    • Miller, J.J.1    Wang, S.2
  • 50
    • 44449092531 scopus 로고    scopus 로고
    • A three-dimensional model of cellular electrical activity
    • Mori Y., Jerome J.W., Peskin C.S. A three-dimensional model of cellular electrical activity. Bull. Inst. Math. Acad. Sin. 2007, 2(2):367-390.
    • (2007) Bull. Inst. Math. Acad. Sin. , vol.2 , Issue.2 , pp. 367-390
    • Mori, Y.1    Jerome, J.W.2    Peskin, C.S.3
  • 51
    • 85015432804 scopus 로고    scopus 로고
    • A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at internal membranes
    • Mori Y., Peskin C.S. A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at internal membranes. Commun. Appl. Math. Comput. Sci. 2009.
    • (2009) Commun. Appl. Math. Comput. Sci.
    • Mori, Y.1    Peskin, C.S.2
  • 53
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Springer-Verlag, Berlin, I. Galligani, E. Magenes (Eds.)
    • Raviart P.A., Thomas J.M. A mixed finite element method for second order elliptic problems. Mathematical Aspects of Finite Element Methods I 1977, Springer-Verlag, Berlin. I. Galligani, E. Magenes (Eds.).
    • (1977) Mathematical Aspects of Finite Element Methods I
    • Raviart, P.A.1    Thomas, J.M.2
  • 54
    • 0142014321 scopus 로고
    • Dual finite element methods for second order elliptic problems
    • John Wiley and Sons Ltd., New York, R. Glowinski, E.Y. Rodin, O.C. Zienkiewicz (Eds.)
    • Raviart P.A., Thomas J.M. Dual finite element methods for second order elliptic problems. Energy Methods in Finite Element Analysis 1979, John Wiley and Sons Ltd., New York. R. Glowinski, E.Y. Rodin, O.C. Zienkiewicz (Eds.).
    • (1979) Energy Methods in Finite Element Analysis
    • Raviart, P.A.1    Thomas, J.M.2
  • 58
    • 0031388772 scopus 로고    scopus 로고
    • Stabilized mixed finite volume methods for convection-diffusion problems
    • Sacco R., Saleri F. Stabilized mixed finite volume methods for convection-diffusion problems. East West J. Numer. Math. 1997, 5(4):291-311.
    • (1997) East West J. Numer. Math. , vol.5 , Issue.4 , pp. 291-311
    • Sacco, R.1    Saleri, F.2
  • 59
    • 84916389355 scopus 로고
    • Large signal analysis of a silicon Read diode oscillator
    • Scharfetter D.L., Gummel H.K. Large signal analysis of a silicon Read diode oscillator. IEEE Trans. Electron Dev. 1969, ED-16:64-77.
    • (1969) IEEE Trans. Electron Dev. , vol.16 ED , pp. 64-77
    • Scharfetter, D.L.1    Gummel, H.K.2
  • 60
    • 0035122587 scopus 로고    scopus 로고
    • Recombinant maxi-K channels on transistor, a prototype of iono-electronic interfacing
    • Straub B., Meyer E., Fromherz P. Recombinant maxi-K channels on transistor, a prototype of iono-electronic interfacing. Nat. Biotechnol. 2001, 19:121-124.
    • (2001) Nat. Biotechnol. , vol.19 , pp. 121-124
    • Straub, B.1    Meyer, E.2    Fromherz, P.3
  • 63
    • 0033450269 scopus 로고    scopus 로고
    • A monotone finite element scheme for convection-diffusion equations
    • Xu J., Zikatanov L. A monotone finite element scheme for convection-diffusion equations. Math. Comput. 1999, 68(228):1429-1446.
    • (1999) Math. Comput. , vol.68 , Issue.228 , pp. 1429-1446
    • Xu, J.1    Zikatanov, L.2
  • 64
    • 0035964350 scopus 로고    scopus 로고
    • Noninvasive neuroelectronic interfacing with synaptically connected snail neurons on a semiconductor chip
    • Zeck G., Fromherz P. Noninvasive neuroelectronic interfacing with synaptically connected snail neurons on a semiconductor chip. PNAS 2001, 98:10457-10462.
    • (2001) PNAS , vol.98 , pp. 10457-10462
    • Zeck, G.1    Fromherz, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.