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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 1, page 189-206
- ISSN: 0764-583X

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topChrysafinos, Konstantinos. "Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's." ESAIM: Mathematical Modelling and Numerical Analysis 44.1 (2010): 189-206. <http://eudml.org/doc/250854>.

@article{Chrysafinos2010,

abstract = {
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 points under
minimal regularity assumptions, and a discrete compactness
argument for discontinuous Galerkin schemes (see Walkington
[SINUM (June 2008) (submitted), preprint available at http://www.math.cmu.edu/~noelw], Sects. 3, 4).
},

author = {Chrysafinos, Konstantinos},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Discontinuous Galerkin approximations;
distributed controls; stability estimates; semi-linear parabolic
PDE's.; distributed controls; semi-linear parabolic PDE's; optimal control; discontinuous Galerkin finite element method; convergence},

language = {eng},

month = {3},

number = {1},

pages = {189-206},

publisher = {EDP Sciences},

title = {Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's},

url = {http://eudml.org/doc/250854},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Chrysafinos, Konstantinos

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 44

IS - 1

SP - 189

EP - 206

AB -
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 points under
minimal regularity assumptions, and a discrete compactness
argument for discontinuous Galerkin schemes (see Walkington
[SINUM (June 2008) (submitted), preprint available at http://www.math.cmu.edu/~noelw], Sects. 3, 4).

LA - eng

KW - Discontinuous Galerkin approximations;
distributed controls; stability estimates; semi-linear parabolic
PDE's.; distributed controls; semi-linear parabolic PDE's; optimal control; discontinuous Galerkin finite element method; convergence

UR - http://eudml.org/doc/250854

ER -

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