A parametric finite element method for fourth order geometric evolution equations

From MaRDI portal
Publication:870630

DOI10.1016/j.jcp.2006.07.026zbMath1112.65093OpenAlexW2092509712WikidataQ117202761 ScholiaQ117202761MaRDI QIDQ870630

Harald Garcke, John W. Barrett, Robert Nürnberg

Publication date: 13 March 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10044/1/641




Related Items (78)

A finite element method for electrowetting on dielectricA fitted finite element method for the numerical approximation of void electro-stress migrationOptimal control of volume-preserving mean curvature flowSegmentation and restoration of images on surfaces by parametric active contours with topology changesA Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed CurvesA perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curvesA second order accuracy preserving method for moving contact lines with Stokes flowAn energy-stable parametric finite element method for anisotropic surface diffusionVolume-preserving parametric finite element methods for axisymmetric geometric evolution equationsStable finite element approximations of two-phase flow with soluble surfactantShape optimization of self-avoiding curvesFinite element approximation of a phase field model arising in nanostructure patterningOn the use of a diffuse-interface model for the simulation of rigid particles in two-phase Newtonian and viscoelastic fluidsA high-order level-set method with enhanced stability for curvature driven flows and surface diffusion motionEvolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flowComparison study for level set and direct Lagrangian methods for computing Willmore flow of closed planar curvesNumerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the CurveA Nested Variational Time Discretization for Parametric Anisotropic Willmore FlowArbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfacesAn ALE ESFEM for solving PDEs on evolving surfacesConvergence of a scheme for an elastic flow with tangential mesh movementA Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening FlowA multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewettingUnfitted finite element methods for axisymmetric two-phase flowEnergy dissipative numerical schemes for gradient flows of planar curvesA structure‐preserving finite element approximation of surface diffusion for curve networks and surface clustersAn ALE meshfree method for surface PDEs coupling with forced mean curvature flow“Gradient-free” diffuse approximations of the Willmore functional and Willmore flowA parametric finite element method for solid-state dewetting problems with anisotropic surface energiesA Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion in Three DimensionsParametric finite element approximations for anisotropic surface diffusion with axisymmetric geometryA structure-preserving parametric finite element method for area-conserved generalized curvature flowArbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flowNew Artificial Tangential Motions for Parametric Finite Element Approximation of Surface EvolutionA numerical method for coupled surface and grain boundary motionGeometric numerical integration. Abstracts from the workshop held March 28 -- April 3, 2021 (hybrid meeting)Stability of travelling wave solutions for coupled surface and grain boundary motionEvolution of plane curves with a curvature adjusted tangential velocitySharp-interface approach for simulating solid-state dewetting in two dimensions: A Cahn-hoffman \(\boldsymbol{\xi}\)-vector formulationOn the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flowVariational discretization of axisymmetric curvature flowsNumerical analysis of elastica with obstacle and adhesion effectsParametric approximation of isotropic and anisotropic elastic flow for closed and open curvesUnnamed ItemALE-FEM for Two-Phase and Free Surface Flows with SurfactantsPhase-field approximations of the Willmore functional and flowStable approximations for axisymmetric Willmore flow for closed and open surfacesSome algorithms for the mean curvature flow under topological changesELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINESComputational parametric Willmore flowA Structure-Preserving Parametric Finite Element Method for Surface DiffusionA variational formulation of anisotropic geometric evolution equations in higher dimensionsPreconditioning a class of fourth order problems by operator splittingA grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motionError analysis for the elastic flow of parametrized curvesOn stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growthThe approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistributeAn unfitted finite element method for the numerical approximation of void electromigrationGradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximationA Parametric Finite Element Method for Solid-State Dewetting Problems in Three DimensionsComputational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity EffectsNumerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifoldsNumerical simulations of immiscible fluid clustersIsogeometric analysis of geometric partial differential equationsFinite element methods for fourth order axisymmetric geometric evolution equationsFitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizationsStable Discretizations of Elastic Flow in Riemannian ManifoldsA sharp-interface model and its numerical approximation for solid-state dewetting with axisymmetric geometryA Convergent evolving finite element algorithm for Willmore flow of closed surfacesAn energy stable finite difference method for anisotropic surface diffusion on closed curvesMeshfree methods on manifolds for hydrodynamic flows on curved surfaces: a generalized moving least-squares (GMLS) approachAn energy-stable finite element method for the simulation of moving contact lines in two-phase flowsA new diffuse-interface approximation of the Willmore flowOn the stable numerical approximation of two-phase flow with insoluble surfactantA stable parametric finite element discretization of two-phase Navier-Stokes flowParameter identification problems in the modelling of cell motility3D finite element simulation of the matter flow by surface diffusion using a level set method



Cites Work


This page was built for publication: A parametric finite element method for fourth order geometric evolution equations