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Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation

Konstantinos Chrysafinos — 2004

ESAIM: Control, Optimisation and Calculus of Variations

A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε 0 is examined.

Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

Konstantinos Chrysafinos — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at arbitrary time...

Analysis and finite element error estimates for the velocity tracking problem for Stokes flows a penalized formulation

Konstantinos Chrysafinos — 2010

ESAIM: Control, Optimisation and Calculus of Variations

A distributed optimal control problem for evolutionary Stokes flows is studied a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined. ...

Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos ChrysafinosNoel J. Walkington — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington,   (2006) 2478–2499; Chrysafinos and Walkington,   (2006) 349–366] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates independent of...

Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Konstantinos ChrysafinosSotirios P. FilopoulosTheodosios K. Papathanasiou — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...

Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Konstantinos ChrysafinosSotirios P. FilopoulosTheodosios K. Papathanasiou — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present....

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