Analysis and approximations of an optimal control problem for the Allen-Cahn equation (Q6093389)

scientific article; zbMATH DE number 7746802

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English	Analysis and approximations of an optimal control problem for the Allen-Cahn equation	scientific article; zbMATH DE number 7746802

Statements

instance of

scholarly article

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title

Analysis and approximations of an optimal control problem for the Allen-Cahn equation (English)

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author

Konstantinos Chrysafinos

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Dimitra Plaka

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published in

Numerische Mathematik

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publication date

6 October 2023

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full work available at URL

https://arxiv.org/abs/2202.09149

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zbMATH Keywords

Allen-Cahn equation

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optimal control

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Galerkin scheme

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MaRDI profile type

MaRDI publication profile

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cites work

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Q3558349

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Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's

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Optimal control of time-discrete two-phase flow driven by a diffuse-interface model

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Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows

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<i><b>A posteriori</b></i>error control for the Allen–Cahn problem: circumventing Gronwall's inequality

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A posteriori error estimates and an adaptive finite element method for the Allen-Cahn equation and the mean curvature flow

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Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen–Cahn and Ginzburg–Landau Equations Past Topological Changes

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Quasi-optimal and robust a posteriori error estimates in $L^{\infty}(L^{2})$ for the approximation of Allen-Cahn equations past singularities

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Spectrum for the allen-chan, chan-hillard, and phase-field equations for generic interfaces

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Geometrical Evolution of Developed Interfaces

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Phase transitions and generalized motion by mean curvature

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Convergence Rates of the Allen--Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies

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Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature

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Convergence of the Allen‐Cahn Equation to Multiphase Mean Curvature Flow

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Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations

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Stability analysis and best approximation error estimates of discontinuous time-stepping schemes for the Allen–Cahn equation

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Infinite-dimensional dynamical systems in mechanics and physics.

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Q4039918

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Introduction

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A Note on Existence of Solutions to Control Problems of Semilinear Partial Differential Equations

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The Mathematical Theory of Finite Element Methods

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The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces

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Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation

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Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations

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Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow

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Energy stability and convergence of SAV block-centered finite difference method for gradient flows

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Identifiers

arXiv ID

2202.09149

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Mathematics Subject Classification ID

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10.1007/S00211-023-01374-8

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Sitelinks

Mathematics(1 entry)

mardi Publication:6093389