A posteriori error estimates for \(hp\) finite element solutions of convex optimal control problems (Q534227)

The authors consider the following two-dimensional convex optimal control problem \[ \min_{u\in K}\{g(y)+ h(u)\}, \] subject to the state equation \[ -\text{div}(A\nabla y)= f+ Bu,\quad x\in\Omega, \] with the boundary condition \(y= 0\), \(x\in\delta\Omega\), where \(g\) and \(h\) are given convex functionals, \(K\) is a closed convex set, and \(B\) is a continuous linear operator. For this problem, the authors present a posteriori error analysis for hp finite element approximation.