A Trace Finite Element Method for PDEs on Evolving Surfaces
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Publication:5348258
DOI10.1137/16M1099388zbMath1371.65110arXiv1610.05831OpenAlexW2532816740MaRDI QIDQ5348258
Xianmin Xu, Maxim A. Olshanskii
Publication date: 15 August 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1610.05831
convergencenumerical experimentfast marching methodevolving surfacestrace finite element methodevel set method
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) Boundary value problems on manifolds (58J32)
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Cites Work
- Unnamed Item
- Unnamed Item
- On some linear parabolic PDEs on moving hypersurfaces
- A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant
- A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis
- PDEs on moving surfaces via the closest point method and a modified grid based particle method
- A finite element method for surface PDEs: Matrix properties
- Finite element approximation of elliptic partial differential equations on implicit surfaces
- Classical solutions for diffusion-induced grain-boundary motion
- Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
- An Eulerian formulation for solving partial differential equations along a moving interface
- On surface meshes induced by level set functions
- An adaptive octree finite element method for PDEs posed on surfaces
- A stabilized cut finite element method for partial differential equations on surfaces: the Laplace-Beltrami operator
- Transport and diffusion of material quantities on propagating interfaces via level set methods.
- Evolving surface finite element method for the Cahn-Hilliard equation
- A cut finite element method for coupled bulk-surface problems on time-dependent domains
- Cut finite element modeling of linear membranes
- Full gradient stabilized cut finite element methods for surface partial differential equations
- An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces
- High order unfitted finite element methods on level set domains using isoparametric mappings
- Diffusion on a curved surface coupled to diffusion in the volume: application to cell biology
- A level-set method for interfacial flows with surfactant
- Characteristic cut finite element methods for convection-diffusion problems on time dependent surfaces
- A Higher Order Finite Element Method for Partial Differential Equations on Surfaces
- Eulerian Finite Element Methods for Parabolic Equations on Moving Surfaces
- An Adaptive Surface Finite Element Method Based on Volume Meshes
- Error Analysis of a Space-Time Finite Element Method for Solving PDEs on Evolving Surfaces
- Unfitted Finite Element Methods Using Bulk Meshes for Surface Partial Differential Equations
- A Finite Element Method for Elliptic Equations on Surfaces
- Numerical Methods for Two-phase Incompressible Flows
- Finite elements on evolving surfaces
- A trace finite element method for a class of coupled bulk-interface transport problems
- Analysis of trace finite element methods for surface partial differential equations
- An h-narrow band finite-element method for elliptic equations on implicit surfaces
- The effect of surfactant on the transient motion of Newtonian drops
- Analysis of a High-Order Trace Finite Element Method for PDEs on Level Set Surfaces
- A cut discontinuous Galerkin method for the Laplace–Beltrami operator
- A fast marching level set method for monotonically advancing fronts.
- $L^2$-estimates for the evolving surface finite element method
- Error analysis for an ALE evolving surface finite element method
- On the stable numerical approximation of two-phase flow with insoluble surfactant
- An Eulerian Space-Time Finite Element Method for Diffusion Problems on Evolving Surfaces
- A stabilized finite element method for advection-diffusion equations on surfaces
- Finite element methods for surface PDEs
- Variational problems and partial differential equations on implicit surfaces
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