TY - JOUR
T1 - Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
AU - Merino, Pedro
AU - Tröltzsch, Fredi
AU - Vexler, Boris
PY - 2010
Y1 - 2010
N2 - The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
AB - The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
KW - Finite element approximation
KW - Finitely many pointwise state constraints
KW - Optimal control problem
UR - http://www.scopus.com/inward/record.url?scp=77950159686&partnerID=8YFLogxK
U2 - 10.1051/m2an/2009045
DO - 10.1051/m2an/2009045
M3 - Article
AN - SCOPUS:77950159686
SN - 2822-7840
VL - 44
SP - 167
EP - 188
JO - Mathematical Modelling and Numerical Analysis
JF - Mathematical Modelling and Numerical Analysis
IS - 1
ER -