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

Molecular Based Mathematical Biology (2013)

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

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topM. 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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