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Analysis and approximations of an optimal control problem for the Allen-Cahn equation
Konstantinos Chrysafinos, Dimitra Plaka
The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-…
A posteriori error estimates for the Allen-Cahn problem
Konstantinos Chrysafinos, Emmanuil H. Georgoulis, Dimitra Plaka
This work is concerned with the proof of \emph{a posteriori} error estimates for fully-discrete Galerkin approximations of the Allen-Cahn equation in two and three spatial dimensio…
Stability Analysis and Best Approximation Error Estimates of Discontinuous Time-Stepping Schemes for the Allen-Cahn Equation
Konstantinos Chrysafinos
Fully-discrete approximations of the Allen-Cahn equation are considered. In particular, we consider schemes of arbitrary order based on a discontinuous Galerkin (in time) approach…