Optimal control of geometric partial differential equations
From MaRDI portal
Publication:2235780
DOI10.1016/bs.hna.2020.10.003zbMath1475.49005OpenAlexW4231127400MaRDI QIDQ2235780
Michael Hintermüller, Tobias Keil
Publication date: 21 October 2021
Full work available at URL: https://doi.org/10.1016/bs.hna.2020.10.003
optimal controlnumerical methodmathematical program with equilibrium constraintsdiffuse interface modelsharp interface modelmultiphase fluidsadaptive discretizationgeometric evolutionconstraint degeneracyC stationarity conditionselectro-wetting on dielectric
Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Optimality conditions and duality in mathematical programming (90C46) Variational inequalities (49J40) PDEs in connection with fluid mechanics (35Q35) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Capillarity (surface tension) for incompressible viscous fluids (76D45) Free boundary problems for PDEs (35R35) Liquid-gas two-phase flows, bubbly flows (76T10) Existence theories for optimal control problems involving partial differential equations (49J20) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87) Numerical methods for variational inequalities and related problems (65K15) PDEs in connection with control and optimization (35Q93)
Cites Work
- An Introduction to Variational Inequalities and Their Applications
- 3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
- Two-dimensional nonlocal Cahn–Hilliard–Navier–Stokes systems with variable viscosity, degenerate mobility and singular potential
- Geometrical Evolution of Developed Interfaces
- On the Cahn–Hilliard Equation with Degenerate Mobility
- TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER
- Weak-Duality Based Adaptive Finite Element Methods for PDE-Constrained Optimization with Pointwise Gradient STATE-Constratints
- Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
- Optimal Control of a Free Boundary Problem: Analysis with Second-Order Sufficient Conditions
- Optimal Control in Some Variational Inequalities
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Droplet Footprint Control
- Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Model for Two Fluids with Different Densities
- Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids
- Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System with Nonmatched Fluid Densities
- Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
- Electrowetting with contact line pinning: Computational modeling and comparisons with experiments
- Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
- On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities
- Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
- Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System
- On the Maximality of Sums of Nonlinear Monotone Operators
- ON A „MONOTONICITY” METHOD FOR THE SOLUTION OF NONLINEAR EQUATIONS IN BANACH SPACES
- A theoretical and numerical model for the study of incompressible mixture flows
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
- Distortion compensation as a shape optimisation problem for a sharp interface model
- A bundle-free implicit programming approach for a class of elliptic MPECs in function space
- Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model
- Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities
- Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints
- Diffuse interface modelling of soluble surfactants in two-phase flow
- Elliptic control problems with gradient constraints -- variational discrete versus piecewise constant controls
- A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
- Maximal regularity and asymptotic behavior of solutions for the Cahn-Hilliard equation with dynamic boundary conditions
- Global asymptotic limit of solutions of the Cahn-Hilliard equation
- Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
- A virtual control concept for state constrained optimal control problems
- A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints
- Optimal control of the free boundary in a two-phase Stefan problem
- A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
- Adaptive finite element methods for Cahn-Hilliard equations
- Finite element approximation of a Cahn-Hilliard-Navier-Stokes system
- Mixed finite element method for electrowetting on dielectric with contact line pinning
- A shape and topology optimization technique for solving a class of linear complementarity problems in function space
- Finite element approximation of elliptic control problems with constraints on the gradient
- On the Cahn-Hilliard equation
- A generalized diffusion model for growth and dispersal in a population
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Generation and propagation of interfaces for reaction-diffusion equations
- Optimal control of nonsmooth distributed parameter systems
- Contrôle dans les inéquations variationelles elliptiques
- Regularity and stability for the mathematical programming problem in Banach spaces
- Model predictive control: Theory and practice - a survey
- Nonsmooth approach to optimization problems with equilibrium constraints. Theory, applications and numerical results
- An introduction to \(\Gamma\)-convergence
- Anisotropic motion by mean curvature in the context of Finsler geometry
- Optimal control of an obstacle problem
- Optimal control of elliptic variational inequalities
- A sharp-interface model coupling VOSET and IBM for simulations on melting and solidification
- Analysis and control of nonlinear infinite dimensional systems
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- The gradient theory of phase transitions and the minimal interface criterion
- A level set approach for the solution of a state-constrained optimal control problem
- Theory and practice of finite elements.
- Convergence of the Cahn-Hilliard equation to the Mullins-Sekerka problem in spherical symmetry
- Combined effect of explicit time-stepping and quadrature for curvature driven flows
- A posteriori error analysis of space-time finite element discretizations of the time-dependent Stokes equations
- A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn-Hilliard-Navier-Stokes system
- An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system
- A sharp-interface model and its numerical approximation for solid-state dewetting with axisymmetric geometry
- Finite horizon model predictive control of electrowetting on dielectric with pinning
- On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility
- Diffuse interface model for incompressible two-phase flows with large density ratios
- Mesh adaptivity in optimal control of elliptic variational inequalities with point-tracking of the state
- On the maximal monotonicity of subdifferential mappings
- Nonlinear variational inequalities and maximal monotone mappings in Banach spaces
- Models of phase transitions
- Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
- Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions
- Towards M-stationarity for Optimal Control of the Obstacle Problem with Control Constraints
- Distributed Optimal Control of the Cahn–Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density
- THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
- Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials
- Shapes and Geometries
- Goal-Oriented Adaptivity in Pointwise State Constrained Optimal Control of Partial Differential Equations
- Numerical computation of advection and diffusion on evolving diffuse interfaces
- Optimal Shape Design Subject to Elliptic Variational Inequalities
- An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem
- Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
- A posterioriestimates for the Cahn–Hilliard equation with obstacle free energy
- Fast Reaction, Slow Diffusion, and Curve Shortening
- Front migration in the nonlinear Cahn-Hilliard equation
- Quantitative benchmark computations of two-dimensional bubble dynamics
- Ana posteriorierror analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
- Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm
- Optimal Control of the Propagation of a Graph in Inhomogeneous Media
- Optimal control of the free boundary in a two-phase Stefan problem with flow driven by convection
- Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints
- Finite Element Methods for Navier-Stokes Equations
- Free boundary problems for minimal surfaces and related questions
- Optimal Control for Variational Inequalities
- Quelques proprietes des applications de trace dance des espaces de champs de vecteurs a divergence nulle
- The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
- Feedback stabilization and optimal control for the Cahn-Hilliard equation
- Phase transitions and generalized motion by mean curvature
- Quasi–incompressible Cahn–Hilliard fluids and topological transitions
- Asymptotics for a parabolic double obstacle problem
- Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
