A Nitsche-type variational formulation for the shape deformation of a single component vesicle

Tae Yeon Kim; Wen Jiang; Sungmun Lee; Jeong Hoon Song; Chan Yeob Yeun; Eun Jae Park

doi:10.1016/j.cma.2019.112661

A Nitsche-type variational formulation for the shape deformation of a single component vesicle

Tae Yeon Kim, Wen Jiang, Sungmun Lee, Jeong Hoon Song, Chan Yeob Yeun, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

This paper concerns the development of a finite-element formulation using Nitsche’ method for the phase-field model to capture an equilibrium shape of a single component vesicle. The phase-field model derived from the minimization of the curvature energy results in a nonlinear fourth-order partial differential equation. A standard conforming Galerkin formulation thus requires C¹-elements. We derive a nonconforming finite-element formulation that can be applied to C⁰-elements and prove its consistency. Continuity of the first derivatives across interelement boundaries is weakly imposed and stabilization of the method is achieved via Nitsche's method. The capability of the proposed finite-element formulation is demonstrated through numerical study of the equilibrium shapes of axisymmetric single component vesicles along with budding and fission phenomena.

Original language	English
Article number	112661
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	359
DOIs	https://doi.org/10.1016/j.cma.2019.112661
Publication status	Published - 2020 Feb 1

Bibliographical note

Funding Information:
T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002 ) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates ( AARE17-069 ). E.-J. Park was supported by NRF, Korea - 2015R1A5A1009350 and NRF, Korea - 2019R1A2C2090021 .

Funding Information:
T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates (AARE17-069). E.-J. Park was supported by NRF, Korea-2015R1A5A1009350 and NRF, Korea -2019R1A2C2090021.

Publisher Copyright:
© 2019 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/j.cma.2019.112661

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title = "A Nitsche-type variational formulation for the shape deformation of a single component vesicle",

abstract = "This paper concerns the development of a finite-element formulation using Nitsche{\textquoteright} method for the phase-field model to capture an equilibrium shape of a single component vesicle. The phase-field model derived from the minimization of the curvature energy results in a nonlinear fourth-order partial differential equation. A standard conforming Galerkin formulation thus requires C1-elements. We derive a nonconforming finite-element formulation that can be applied to C0-elements and prove its consistency. Continuity of the first derivatives across interelement boundaries is weakly imposed and stabilization of the method is achieved via Nitsche's method. The capability of the proposed finite-element formulation is demonstrated through numerical study of the equilibrium shapes of axisymmetric single component vesicles along with budding and fission phenomena.",

author = "Kim, {Tae Yeon} and Wen Jiang and Sungmun Lee and Song, {Jeong Hoon} and Yeun, {Chan Yeob} and Park, {Eun Jae}",

note = "Funding Information: T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002 ) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates ( AARE17-069 ). E.-J. Park was supported by NRF, Korea - 2015R1A5A1009350 and NRF, Korea - 2019R1A2C2090021 . Funding Information: T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates (AARE17-069). E.-J. Park was supported by NRF, Korea-2015R1A5A1009350 and NRF, Korea -2019R1A2C2090021. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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N1 - Funding Information: T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002 ) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates ( AARE17-069 ). E.-J. Park was supported by NRF, Korea - 2015R1A5A1009350 and NRF, Korea - 2019R1A2C2090021 . Funding Information: T.-Y. Kim and S.M. Lee gratefully appreciate the support from Khalifa University, United Arab Emirates Internal Research Funding (KURIF Level 2 No. 8474000002) and ADEK Award for Research Excellence (AARE) 2017, United Arab Emirates (AARE17-069). E.-J. Park was supported by NRF, Korea-2015R1A5A1009350 and NRF, Korea -2019R1A2C2090021. Publisher Copyright: © 2019 Elsevier B.V.

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N2 - This paper concerns the development of a finite-element formulation using Nitsche’ method for the phase-field model to capture an equilibrium shape of a single component vesicle. The phase-field model derived from the minimization of the curvature energy results in a nonlinear fourth-order partial differential equation. A standard conforming Galerkin formulation thus requires C1-elements. We derive a nonconforming finite-element formulation that can be applied to C0-elements and prove its consistency. Continuity of the first derivatives across interelement boundaries is weakly imposed and stabilization of the method is achieved via Nitsche's method. The capability of the proposed finite-element formulation is demonstrated through numerical study of the equilibrium shapes of axisymmetric single component vesicles along with budding and fission phenomena.

AB - This paper concerns the development of a finite-element formulation using Nitsche’ method for the phase-field model to capture an equilibrium shape of a single component vesicle. The phase-field model derived from the minimization of the curvature energy results in a nonlinear fourth-order partial differential equation. A standard conforming Galerkin formulation thus requires C1-elements. We derive a nonconforming finite-element formulation that can be applied to C0-elements and prove its consistency. Continuity of the first derivatives across interelement boundaries is weakly imposed and stabilization of the method is achieved via Nitsche's method. The capability of the proposed finite-element formulation is demonstrated through numerical study of the equilibrium shapes of axisymmetric single component vesicles along with budding and fission phenomena.

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A Nitsche-type variational formulation for the shape deformation of a single component vesicle

Abstract

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