Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces
DOI10.1007/s00211-022-01280-5zbMath1491.65089arXiv2006.02274OpenAlexW4225713359MaRDI QIDQ2143151
Balázs Kovács, Cedric Aaron Beschle
Publication date: 31 May 2022
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.02274
Nonlinear parabolic equations (35K55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs on manifolds (35R01)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Scalar conservation laws on moving hypersurfaces
- Isogeometric analysis of the advective Cahn-Hilliard equation: spinodal decomposition under shear flow
- On a generalized Cahn-Hilliard equation with biological applications
- On some linear parabolic PDEs on moving hypersurfaces
- Finite element approximation of the Cahn-Hilliard equation on surfaces
- Existence of solutions to a Cahn-Hilliard type equation with a logarithmic nonlinear term
- Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations
- Linearly implicit full discretization of surface evolution
- Convergence of finite elements on an evolving surface driven by diffusion on the surface
- A Convergent evolving finite element algorithm for Willmore flow of closed surfaces
- Numerical modeling of phase separation on dynamic surfaces
- An isogeometric finite element formulation for phase transitions on deforming surfaces
- Evolving surface finite element method for the Cahn-Hilliard equation
- A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
- The Cahn-Hilliard equation and some of its variants
- An abstract framework for parabolic PDEs on evolving spaces
- Backward difference time discretization of parabolic differential equations on evolving surfaces
- Runge-Kutta time discretization of parabolic differential equations on evolving surfaces
- Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
- G-stability is equivalent toA-stability
- Finite element approximation for the dynamics of fluidic two-phase biomembranes
- Finite elements on evolving surfaces
- Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
- Multiplier techniques for linear multistep methods
- High-order evolving surface finite element method for parabolic problems on evolving surfaces
- Higher order time discretizations with ALE finite elements for parabolic problems on evolving surfaces
- $L^2$-estimates for the evolving surface finite element method
- Cahn–Hilliard equations on an evolving surface
- A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains
- Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Error analysis for an ALE evolving surface finite element method
- Finite element methods for surface PDEs
- The Mathematical Theory of Finite Element Methods
- Variational discretization of wave equations on evolving surfaces
- Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces
This page was built for publication: Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces