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

• Autorzy: M. R. Swager , Y. C. Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Drift-diffusion equations; Exponential fitting; Multidimensional; Divergence-free basis functions; High order methods

• Wydawca: De Gruyter Open
• Czasopismo: Molecular Based Mathematical Biology
• Rocznik: 2013
• Tom: 1
• Strony: 26-41

Daty

otrzymano

2012-10-18

zaakceptowano

2013-02-12

online

2013-03-20

Twórcy

autor

M. R. Swager

autor

Y. C. Zhou

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Identyfikatory

DOI

10.2478/mlbmb-2013-0001