Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature

DOI10.1093/imanum/drx006zbMath1433.65206OpenAlexW2470958303WikidataQ117202071 ScholiaQ117202071MaRDI QIDQ4683803

Robert Nürnberg, Harald Garcke, John W. Barrett

Publication date: 26 September 2018

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10044/1/43913

zbMATH Keywords

clamped boundary conditionsparametric finite elementstangential movementNavier boundary conditionsWillmore flowspontaneous curvatureline energyGaussian curvature energy

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Flows related to mean curvature (53E10)

Related Items

Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour, A Posteriori Error Estimates for the Laplace--Beltrami Operator on Parametric $C^2$ Surfaces, Stable approximations for axisymmetric Willmore flow for closed and open surfaces, Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation, Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects, Finite element methods for fourth order axisymmetric geometric evolution equations