A formula for membrane mediated point particle interactions on near spherical biomembranes

DOI10.4171/IFB/464zbMath1486.35175arXiv2012.04587OpenAlexW3112634183MaRDI QIDQ2119722

Philip J. Herbert, Charles M. Elliott

Publication date: 30 March 2022

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.04587

zbMATH Keywords

mixed finite elementsCanham-Helfrich energymembrane mediated interaction

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Variational methods for higher-order elliptic equations (35J35)

Uses Software

• ALUGrid
• DUNE-ALUGrid
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Cites Work

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• The \textsc{Dune} framework: basic concepts and recent developments
• Direct Methods in the Theory of Elliptic Equations
• Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
• Domain formation via phase separation for spherical biomembranes with small deformations
• Second order splitting of a class of fourth order PDEs with point constraints
• Second order splitting for a class of fourth order equations
• A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces
• Finite element methods for surface PDEs
• Discretization error estimates for penalty formulations of a linearized Canham–Helfrich-type energy
• Stream function formulation of surface Stokes equations
• Ordinary Differential Equations

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