A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints

Abstract

We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficients in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.

Keywords

• Elliptic Neumann boundary control problems
• Pointwise control constraints
• Finite element methods
• Rough coefficients
• Multiscale