Monotone multigrid methods for elliptic variational inequalities I
Numerische Mathematik
On the Cahn-Hilliard equation with degenerate mobility
SIAM Journal on Mathematical Analysis
Journal of Computational Physics
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System
SIAM Journal on Numerical Analysis
Mathematics of Computation
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
Finite element approximation of a sixth order nonlinear degenerate parabolic equation
Numerische Mathematik
A finite element method for surface diffusion: the parametric case
Journal of Computational Physics
Finite Element Approximation of Soluble Surfactant Spreading on a Thin Film
SIAM Journal on Numerical Analysis
Numerical Analysis of Vanka-Type Solvers for Steady Stokes and Navier-Stokes Flows
SIAM Journal on Numerical Analysis
On the parametric finite element approximation of evolving hypersurfaces in R3
Journal of Computational Physics
Phase field computations for surface diffusion and void electromigration in $${\mathbb{R}^3}$$
Computing and Visualization in Science
Numerical simulations of immiscible fluid clusters
Applied Numerical Mathematics
A multigrid solver for phase field simulation of microstructure evolution
Mathematics and Computers in Simulation
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We consider a finite element approximation of a phase field model for the evolution of voids by surface diffusion in an electrically conducting solid. The phase field equations are given by the nonlinear degenerate parabolic system $$\gamma\frac{\partial u}{\partial t}-\nabla.(b(u)\nabla[w+\alpha\phi])=0,\qquad w=-\gamma\Delta u+\gamma^{-1}\Psi'(u),\qquad\nabla.(c(u)\nabla\phi)=0$$ subject to an initial condition u 0(驴)驴[驴1,1] on u and flux boundary conditions on all three equations. Here 驴驴驴0, 驴驴驴驴0, 驴 is a non-smooth double well potential, and c(u):=1+u, b(u):=1驴u 2 are degenerate coefficients. On extending existing results for the simplified two dimensional phase field model, we show stability bounds for our approximation and prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in three space dimensions. Furthermore, a new iterative scheme for solving the resulting nonlinear discrete system is introduced and some numerical experiments are presented.