Repository: Freie Universität Berlin, Math Department

Discretization Error Estimates for Penalty Formulations of a Linearized Canham-Helfrich Type Energy

Gräser, C. and Kies, T. (2017) Discretization Error Estimates for Penalty Formulations of a Linearized Canham-Helfrich Type Energy. SFB 1114 Preprint .

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Official URL: https://arxiv.org/abs/1703.06688

Abstract

This paper is concerned with minimization of a fourth-order linearized Canham-Helfrich 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 almost-H^5/2 regularity of the solution and then consider two possible penalty formulations. For the combination of these penalty formulations with a Bogner-Fox-Schmit 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 re-meshing 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:22 May 2017 09:02

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