A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions

The present work is devoted to the a posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Using the duality technique we derive a reliable and efficient a posteriori error estimator that measures the error in the energy norm. The estimator can be used in assessing the error of any approximate solution which belongs to the Sobolev space H1, independently of the discretization method chosen. Only two global constants appear in the definition of the estimator; both constants depend solely on the domain geometry, and the estimator is quite nonsensitive to the error in the constants evaluation. It is also shown how accurately the estimator captures the local error distribution, thus, creating a base for a justified adaptivity of an approximation.