Comparative study of finite element formulations for the semiconductor drift-diffusion equations

1997 ◽  
Vol 40 (18) ◽  
pp. 3405-3419 ◽  
Author(s):  
J. T. Trattles ◽  
C. M. Johnson
Keyword(s):  
Finite Element ◽  
Comparative Study ◽  
Diffusion Equations ◽  
Drift Diffusion ◽  
Finite Element Formulations

Efficient Higher Order Nodal Finite Element Formulations for Neutron Multigroup Diffusion Equations

1996 ◽  
Vol 124 (1) ◽  
pp. 97-110 ◽  
Author(s):  
J. P. Hennart ◽  
E. M. Malambu ◽  
E. H. Mund ◽  
E. del Valle
Keyword(s):  
Finite Element ◽  
Higher Order ◽  
Diffusion Equations ◽  
Finite Element Formulations

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

2013 ◽  
Vol 1 ◽  
pp. 26-41
Author(s):  
M. R. Swager ◽  
Y. C. Zhou
Keyword(s):  
Finite Element ◽  
High Order ◽  
Basis Functions ◽  
Diffusion Equations ◽  
Polynomial Space ◽  
Drift Diffusion ◽  
First Order ◽  
Finite Element Approximations ◽  
Exponentially Fitted ◽  
The One

AbstractA 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.

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