Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints

96 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS AND ITS SEMI-DISCRETE APPROXIMATIONS (2006, background): “Recently important progresses have done at this respect in the context of optimal control problems for semilinear elliptic equations ([29], [30]).”
Finite element error analysis for state-constrained optimal control of the Stokes equations (2008, background): “We exemplarily mention Casas [8], where a semilinear elliptic control problem with finitely many state constraints is considered, and Casas and Mateos [9], where convergence of a finite element discretization for stateconstrained semilinear elliptic problems is proved in a general setting.”
Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods (2005, methodology): “Recently important progress has been made in this respect in the context of optimal control problems for semilinear elliptic equations (see [14, 15]).”
A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM (2009, background): “Casas proved convergence of finite element approximations to optimal control problems for semi-linear elliptic equations with finitely many state constraints in [8].”