Related papers: An evolving surface finite element method for the …
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully…
We use the evolving surface finite element method to solve a Cahn- Hilliard equation on an evolving surface with prescribed velocity. We start by deriving the equation using a conservation law and appropriate transport for- mulae and…
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…
In two recent publications [Kov{\'a}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong convergence of the semi-discrete and fully discrete…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in time and correlated in space. The stochastic Cahn-Hilliard…
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathbb{R}^3$ under discretisation. We also provide a…
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…
In this work, we propose a numerical method based on high degree continuous nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the finite element method proves to be very efficient and favorably compares with other…
In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…
We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…