3 research outputs found
Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations
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-one
correspondence between continuous piecewise polynomial space of degree
and the divergence-free vector space of degree , one can construct
high-order 2-D 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
at two different node set
Electrodiffusion on the surface of bilayer membranes
2012 Spring.Includes bibliographical references.The cell memebrane is of utmost importance in the transportation of nutrients to the cell which are needed for survival. The magnitude of this is the inspiration for our study of the lipid bilayer which forms the cell membrane. In this paper we present a continuum model of electrodiffusion of lipids on the surface of bilayer membranes. Offering three derivations of the surface electrodiffusion equation, and proofs for the existence and uniqueness of the solution. A method for calculating integration constants using slotboom variables is emloyed. The development of a linear surface finite element method to solve the surface electrodiffusion equation is presented. Numerical simulations implementing the model are also given. The stability of the model is analyzed and a stability scheme using Streamline Upwind Petrov-Galerkin equations is applied. We test our code for robustness using other examples and a complex mesh. The implementation is validated by comparing with the known solution for the equations