A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
SIAM Journal on Numerical Analysis
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
Fast Iterative Solvers for Discrete Stokes Equations
SIAM Journal on Scientific Computing
A multigrid finite element solver for the Cahn-Hilliard equation
Journal of Computational Physics
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
Efficient Numerical Solution of Cahn-Hilliard-Navier-Stokes Fluids in 2D
SIAM Journal on Scientific Computing
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Analysis of an extended pressure finite element space for two-phase incompressible flows
Computing and Visualization in Science
Nonsmooth Newton Methods for Set-Valued Saddle Point Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Preconditioning Saddle-Point Systems with Applications in Optimization
SIAM Journal on Scientific Computing
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
Computational Optimization and Applications
An adaptive finite-element Moreau-Yosida-based solver for a non-smooth Cahn-Hilliard problem
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
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An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn-Hilliard/Navier-Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed. A semi-implicit Euler scheme for the time-integration is applied which results in a system coupling a quasi-Stokes or Oseen-type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the Cahn-Hilliard model [16]. A Moreau-Yosida regularization is employed which relaxes the constraints contained in the variational inequality and, thus, enables semi-smooth Newton solvers with locally superlinear convergence in function space. Moreover, upon discretization this yields a mesh independent method for a fixed relaxation parameter. For the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used, and for the numerical approximation of the fluid velocity Taylor-Hood finite elements are employed. The paper ends by a report on numerical examples showing the efficiency of the new method.