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

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Swager M. R., Zhou Y. C.

Molecular Based Mathematical Biology

2013

tom 1

26-41

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.

Ograniczanie wyników

1 Molecular Based Mathematical Biology

1 Swager M. R.

1 Zhou Y. C.

1 2013

Wyniki wyszukiwania

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