Adkins, Melissa, authorZhou, Yongcheng, advisorKrapf, Diego, committee memberLiu, James, committee memberMueller, Jennifer, committee member2015-08-272015-08-272015http://hdl.handle.net/10217/166986The cell membrane is of utmost importance in the transportation of nutrients and signals 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. It has been recently accepted that the lipid bilayer consists of lipid microdomains (lipid rafts), as opposed to freely moving lipids. We present two lipid raft models using the Ginzburg-Landau energy with addition of the electrostatic energy and the geodesic curvature energy to describe the local pattern formation of these lipid rafts. The development and implementation of a C⁰ interior penalty surface finite element method along with an implicit time iteration scheme will also be discussed as the optimal solution technique.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Text