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$hp$-Discontinuous Galerkin methods for the Lotka-McKendrick equation: A numerical study

김미영|정신자|Tsendanysh Selenge
대한수학회 (The Korean Mathematical Society)|2007.10|대한수학회논문집 (Communications of the KMS)|제22권 제4호|pp. 623-640

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Abstract

The Lotka-McKendrick model which describes the evolutionof a single population is developed from the well known Malthus model. Inthis paper, we introduce the Lotka-McKendrick model. We approximatethe solution to the model using hp-discontinuous Galerkin nite elementmethod. The numerical results show that the presented hp-discontinuousGalerkin method is very ecient in case that the solution has a sharpdecay.

참고문헌 (11)

  1. "Numerical Analysis for Applied Science" (1998), John Wiley &Sons
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  3. "Numerical Solution of Partial Dierential Equations by the Finite ElementMethod" (1987), The Cambridge University Press
  4. "A collocation method for the GurtinMacCamy equation with nite life-span", 39(6), pp.1914~1937 (2002)
  5. "Discontinuous Galerkin methods for a model of population dynamics with un-bounded mortality", 27(4), pp.1371~1393 (2006)
  6. "Discontinuous Galerkin methods for the Lotka-Mckendrick equation with nitelife-span", 16(2), pp.161~176 (2006)
  7. "Selenge,Age-Time Discontinuous Method for the Lotka-McKendrickEquation", 18(3), pp.569~580 (2003)
  8. "Fink,Numerical Methods using Matlab" (1999), Prentice-Hall
  9. "hp-Finite Element Methods for Singular Perturbations" (2002), Springer
  10. "p- and hp-Finite Element Methods: Theory and Applications in Solid andFluid Mechanics" (1998), Oxford University Press Inc.
  11. "Galerkin Finite Element Methods for Parabolic Problems", pp.640~ (1997), Springer Seriesin Computational Mathematics, Springer

관련 논문AI추천

Age-time discontinuous Galerkin method for the Lotka-McKendrick equationMi-Young Kim, Ts. Selenge대한수학회 · 대한수학회논문집2003 · 제18권 제3호A discontinuous Galerkin method for a model of population dynamicsMi-Young Kim, Y. X. Yin대한수학회 · 대한수학회논문집2003 · 제18권 제4호L^2-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations엄미례, 이현영대한수학회 · 대한수학회보2011 · 제48권 제5호Error estimates for fully discrete mixed discontinuous Galerkin approximations for parabolic problems신준용, 엄미례, 이현영영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호ERROR ESTIMATES FOR A SEMI-DISCRETE MIXED DISCONTINUOUS GALERKIN METHOD WITH AN INTERIOR PENALTY FOR PARABOLIC PROBLEMS신준용, 엄미례, 이현영영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호Analysis of a Meshfree Method for the compressible Euler Equations김용식, 박대현대한수학회 · 대한수학회지2006 · 제43권 제5호

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