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Qiang Du Liyong Zhu 《计算数学(英文版)》2006,24(3):265-280
In this paper, we study numerical approximations of a recently proposed phase fieldmodel for the vesicle membrane deformation governed by the variation of the elastic bend-ing energy. To overcome the challenges of high order nonlinear differential systems and thenonlinear constraints associated with the problem, we present the phase field bending elas-ticity model in a nested saddle point formulation. A mixed finite element method is thenemployed to compute the equilibrium configuration of a vesicle membrane with prescribedvolume and surface area. Coupling the approximation results for a related linearized prob-lem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for thefinite element approximations of the phase field model are obtained. Numerical results areprovided to substantiate the derived estimates. 相似文献
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