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Volumn 27, Issue 2, 2007, Pages 332-365

Conservative upwind finite-element method for a simplified Keller-Segel system modelling chemotaxis

Author keywords

Analytic semigroup; Conservation of mass; Conservation of positivity; Finite element method; Non linear evolution equation; Parabolic Elliptic system

Indexed keywords

BIOCHEMISTRY; TRIANGULATION;

EID: 34047151167     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drl018     Document Type: Article
Times cited : (94)

References (35)
  • 2
    • 0001782272 scopus 로고
    • On a conservative upwind finite element scheme for convective diffusion equations
    • BABA, K. & TABATA, M. (1981) On a conservative upwind finite element scheme for convective diffusion equations. RAIRO Anal. Numér., 15, 3-25.
    • (1981) RAIRO Anal. Numér , vol.15 , pp. 3-25
    • BABA, K.1    TABATA, M.2
  • 3
    • 0141976345 scopus 로고    scopus 로고
    • Maximum-norm estimates for resolvents of elliptic finite element operators
    • BAKAEV, N. Y., THOMÉE, V. & WAHLBIN, L. B. (2003) Maximum-norm estimates for resolvents of elliptic finite element operators. Math. Comput., 72, 1597-1610.
    • (2003) Math. Comput , vol.72 , pp. 1597-1610
    • BAKAEV, N.Y.1    THOMÉE, V.2    WAHLBIN, L.B.3
  • 4
    • 0000657461 scopus 로고    scopus 로고
    • Local and global solvability of some parabolic systems modelling chemotaxis
    • BILER, B. (1998) Local and global solvability of some parabolic systems modelling chemotaxis. Adv. Math. Sci. Appl., 8, 715-743.
    • (1998) Adv. Math. Sci. Appl , vol.8 , pp. 715-743
    • BILER, B.1
  • 5
    • 0000219814 scopus 로고
    • The Debye system: Existence and large time behavior of solutions
    • BILER, P., HEBISCH, W. & NADZIEJA, T. (1994) The Debye system: existence and large time behavior of solutions. Nonlinear Anal., 23, 1189-1209.
    • (1994) Nonlinear Anal , vol.23 , pp. 1189-1209
    • BILER, P.1    HEBISCH, W.2    NADZIEJA, T.3
  • 6
    • 0000531920 scopus 로고
    • Existence and nonexistence of solutions for a model of gravitational interaction of particles. I
    • BILER, P. & NADZIEJA, T. (1994) Existence and nonexistence of solutions for a model of gravitational interaction of particles. I. Colloq. Math., 66, 319-334.
    • (1994) Colloq. Math , vol.66 , pp. 319-334
    • BILER, P.1    NADZIEJA, T.2
  • 9
    • 84966243417 scopus 로고
    • 2-projection onto finite element function spaces
    • 2-projection onto finite element function spaces. Math. Comput., 48, 521-532.
    • (1987) Math. Comput , vol.48 , pp. 521-532
    • CROUZEIX, M.1    THOMÉE, V.2
  • 10
    • 85016194940 scopus 로고    scopus 로고
    • p for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes
    • p for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes. Comput. Methods Appl. Math., 1, 3-17.
    • (2001) Comput. Methods Appl. Math , vol.1 , pp. 3-17
    • CROUZEIX, M.1    THOMÉE, V.2
  • 11
    • 85120507707 scopus 로고    scopus 로고
    • 2-projection into finite element function spaces. Numer. Math., 23, 193-197.
    • 2-projection into finite element function spaces. Numer. Math., 23, 193-197.
  • 12
    • 0005657125 scopus 로고
    • Some remarks on finite element analysis of time-dependent field problems
    • Y. Yamada & R. H. Gallagher eds, Tokyo: University of Tokyo Press, pp
    • FUJII, H. (1973) Some remarks on finite element analysis of time-dependent field problems. Theory and Practice in Finite Element Structural Analysis (Y. Yamada & R. H. Gallagher eds). Tokyo: University of Tokyo Press, pp. 91-106.
    • (1973) Theory and Practice in Finite Element Structural Analysis , pp. 91-106
    • FUJII, H.1
  • 15
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • New York: Springer
    • HENRY, D. (1981) Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, vol. 840. New York: Springer.
    • (1981) Lecture Notes in Mathematics , vol.840
    • HENRY, D.1
  • 16
    • 4744373150 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I
    • HORSTMANN, D. (2003) From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I. Jahresber. Dtsch. Math.Ver., 105, 103-165.
    • (2003) Jahresber. Dtsch. Math.Ver , vol.105 , pp. 103-165
    • HORSTMANN, D.1
  • 17
    • 13844288282 scopus 로고    scopus 로고
    • From 1970 until present: The Keller-Segel model in chemotaxis and its consequences II
    • HORSTMANN, D. (2004) From 1970 until present: the Keller-Segel model in chemotaxis and its consequences II. Jahresber. Dtsch. Math.Ver., 106, 51-69.
    • (2004) Jahresber. Dtsch. Math.Ver , vol.106 , pp. 51-69
    • HORSTMANN, D.1
  • 19
    • 0014748565 scopus 로고
    • Initiation on slime mold aggregation viewed as instability
    • KELLER, E. F. & SEGEL, L. A. (1970) Initiation on slime mold aggregation viewed as instability. J. Theor. Biol., 26, 399-415.
    • (1970) J. Theor. Biol , vol.26 , pp. 399-415
    • KELLER, E.F.1    SEGEL, L.A.2
  • 20
    • 34047154777 scopus 로고    scopus 로고
    • KREIN, S. G. (1972) Linear Differential Equations in Banach Space. Providence, RI: AMS. (Translated from the Russian by J. M. Danskin.)
    • KREIN, S. G. (1972) Linear Differential Equations in Banach Space. Providence, RI: AMS. (Translated from the Russian by J. M. Danskin.)
  • 21
    • 0344629886 scopus 로고    scopus 로고
    • Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
    • MARROCCO, A. (2003) Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. M2AN Math. Model Numer. Anal., 37, 617-630.
    • (2003) M2AN Math. Model Numer. Anal , vol.37 , pp. 617-630
    • MARROCCO, A.1
  • 22
    • 0141533339 scopus 로고    scopus 로고
    • Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems
    • NAKAGUCHI, E. & YAGI, Y. (2002) Fully discrete approximation by Galerkin Runge-Kutta methods for quasilinear parabolic systems. Hokkaido Math. J., 2002, 385-429.
    • (2002) Hokkaido Math. J , vol.2002 , pp. 385-429
    • NAKAGUCHI, E.1    YAGI, Y.2
  • 23
    • 0348110762 scopus 로고
    • On the semidiscrete finite element approximation for the nonstationary Navier-Stokes equation
    • OKAMOTO, H. (1982) On the semidiscrete finite element approximation for the nonstationary Navier-Stokes equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 29, 613-651.
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA Math , vol.29 , pp. 613-651
    • OKAMOTO, H.1
  • 24
    • 3042643333 scopus 로고    scopus 로고
    • A holomorphic semigroup approach to the lumped mass finite element method
    • SAITO, N. (2004a) A holomorphic semigroup approach to the lumped mass finite element method. J. Comput. Appl. Math., 169, 71-85.
    • (2004) J. Comput. Appl. Math , vol.169 , pp. 71-85
    • SAITO, N.1
  • 25
    • 8744278184 scopus 로고    scopus 로고
    • Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions
    • SAITO, N. (2004b) Remarks on the rational approximation of holomorphic semigroups with nonuniform partitions. Jpn. J. Ind. Appl. Math., 21, 323-337.
    • (2004) Jpn. J. Ind. Appl. Math , vol.21 , pp. 323-337
    • SAITO, N.1
  • 26
    • 28444472731 scopus 로고    scopus 로고
    • Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis
    • SAITO, N. & SUZUKI, T. (2005) Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis. Appl. Math. Comput., 171, 72-90.
    • (2005) Appl. Math. Comput , vol.171 , pp. 72-90
    • SAITO, N.1    SUZUKI, T.2
  • 27
    • 0040426419 scopus 로고    scopus 로고
    • Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids. I. Global estimates
    • SCHATZ, A. H. (1998) Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids. I. Global estimates. Math. Comput., 67, 877-899.
    • (1998) Math. Comput , vol.67 , pp. 877-899
    • SCHATZ, A.H.1
  • 28
    • 34047155861 scopus 로고
    • On LP estimates and regularity. I
    • SCHECHTER, M. (1963) On LP estimates and regularity. I. Am. J. Math., 85, 1-13.
    • (1963) Am. J. Math , vol.85 , pp. 1-13
    • SCHECHTER, M.1
  • 29
    • 0003242729 scopus 로고
    • On Dirichlet's Boundary Value Problem
    • New York: Springer
    • SIMADER, C. G. (1972) On Dirichlet's Boundary Value Problem. Lecture Notes in Mathematics, vol. 268. New York: Springer.
    • (1972) Lecture Notes in Mathematics , vol.268
    • SIMADER, C.G.1
  • 34
    • 0001488448 scopus 로고    scopus 로고
    • Norm behavior of solutions to a parabolic system of chemotaxis
    • YAGI, A. (1997) Norm behavior of solutions to a parabolic system of chemotaxis. Math. Japon., 45, 241-265.
    • (1997) Math. Japon , vol.45 , pp. 241-265
    • YAGI, A.1
  • 35
    • 0003943048 scopus 로고    scopus 로고
    • 2nd revised and expanded edn. Berlin: Springer
    • VARGA, R. S. (2000) Matrix Iterative Analysis, 2nd revised and expanded edn. Berlin: Springer.
    • (2000) Matrix Iterative Analysis
    • VARGA, R.S.1


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