Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations

M. R. Swager; Y. C. Zhou

Molecular Based Mathematical Biology (2013)

  • Volume: 1, page 26-41
  • ISSN: 2299-3266

Abstract

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A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion processes. Such methods are highly desirable for achieving numerical stability and efficiency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of degree k, one can construct high-order two-dimensional exponentially fitted basis functions that are strictly interpolative at a selected node set but are discontinuous on edges in general, spanning nonconforming finite element spaces. First order convergence was proved for the methods constructed from divergence-free Raviart-Thomas space RT 00 at two different node sets.

How to cite

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M. R. Swager, and Y. C. Zhou. "Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations." Molecular Based Mathematical Biology 1 (2013): 26-41. <http://eudml.org/doc/267279>.

@article{M2013,
abstract = {A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion processes. Such methods are highly desirable for achieving numerical stability and efficiency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of degree k, one can construct high-order two-dimensional exponentially fitted basis functions that are strictly interpolative at a selected node set but are discontinuous on edges in general, spanning nonconforming finite element spaces. First order convergence was proved for the methods constructed from divergence-free Raviart-Thomas space RT 00 at two different node sets.},
author = {M. R. Swager, Y. C. Zhou},
journal = {Molecular Based Mathematical Biology},
keywords = {Drift-diffusion equations; Exponential fitting; Multidimensional; Divergence-free basis functions; High order methods; drift-diffusion equations; exponential fitting; multi-dimensional drift-diffusion equations; divergence-free basis functions; high order methods},
language = {eng},
pages = {26-41},
title = {Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations},
url = {http://eudml.org/doc/267279},
volume = {1},
year = {2013},
}

TY - JOUR
AU - M. R. Swager
AU - Y. C. Zhou
TI - Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations
JO - Molecular Based Mathematical Biology
PY - 2013
VL - 1
SP - 26
EP - 41
AB - A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion processes. Such methods are highly desirable for achieving numerical stability and efficiency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of degree k, one can construct high-order two-dimensional exponentially fitted basis functions that are strictly interpolative at a selected node set but are discontinuous on edges in general, spanning nonconforming finite element spaces. First order convergence was proved for the methods constructed from divergence-free Raviart-Thomas space RT 00 at two different node sets.
LA - eng
KW - Drift-diffusion equations; Exponential fitting; Multidimensional; Divergence-free basis functions; High order methods; drift-diffusion equations; exponential fitting; multi-dimensional drift-diffusion equations; divergence-free basis functions; high order methods
UR - http://eudml.org/doc/267279
ER -

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