Gräser, C. and Kies, T. (2017) Discretization Error Estimates for Penalty Formulations of a Linearized CanhamHelfrich Type Energy. arXiv.com .

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Official URL: https://arxiv.org/abs/1703.06688
Abstract
This paper is concerned with minimization of a fourthorder linearized CanhamHelfrich energy subject to Dirichlet boundary conditions on curves inside the domain. Such problems arise in the modeling of the mechanical interaction of biomembranes with embedded particles. There, the curve conditions result from the imposed particle{membrane coupling. We prove almostH^5/2 regularity of the solution and then consider two possible penalty formulations. For the combination of these penalty formulations with a BognerFoxSchmit finite element discretization we prove discretization error estimates which are optimal in view of the solution's reduced regularity. The error estimates are based on a general estimate for linear penalty problems in Hilbert spaces. Finally, we illustrate the theoretical results by numerical computations. An important feature of the presented discretization is that it does not require to resolve the particle boundary. This is crucial in order to avoid remeshing if the presented problem arises as subproblem in a model where particles are allowed to move or rotate.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2072 
Deposited By:  Silvia Hoemke 
Deposited On:  20 Apr 2017 09:27 
Last Modified:  29 Sep 2017 14:57 
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