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.
@article{bwmeta1.element.doi-10_2478_mlbmb-2013-0001,
author = {M. R. Swager and Y. C. Zhou},
title = {Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations},
journal = {Molecular Based Mathematical Biology},
volume = {1},
year = {2013},
pages = {26-41},
zbl = {1277.65099},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2013-0001}
}
M. R. Swager; Y. C. Zhou. Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations. Molecular Based Mathematical Biology, Tome 1 (2013) pp. 26-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2013-0001/
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