Approximation of sparse controls in semilinear equations by piecewise linear functions
The authors consider a distributed optimal control problem defined by a semilinear elliptic differential equation where the objective functional is non-differentiable. Both the state and the controls are discretized by continuous piecewise linear functions. Then they prove the convergence of the discretization and derive error estimates for the optimal control. These are obtained by an appropriate discretization of the objective functional using a quadrature formulae. Finally, numerical examples confirm the convergence rates.
semilinear elliptic differential equation
scientific article; zbMATH DE number 6117690
scientific article