Mesh-Dependent L2-Like Norm a Posteriori Error Estimates for Elliptic Problems with Non-essential Boundary Conditions

This work is concerned with the proof of L 2 -like norm residual-type a posteriori error estimates for finite element methods for elliptic problems with non-essential boundary conditions, such as Neumann or Robin type. To ensure the proof of lower bounds (efficiency), a non-standard mesh-dependent L 2 -like norm is used for the error. The proof of lower bounds requires a carefully constructed C 1 -conforming ’bubble’-function. A series of numerical experiments is presented, showcasing the good performance of the estimators.