Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation

In this paper, the local averaging based a posteriori finite element error control for a class of nonlinear elliptic equations is investigated. It is shown by both theory and practice that the error control is reliable and the associated adaptive computation is efficient for problems with smooth data. It is also shown by numerical experiments that the error control can be successfully applied to a class of Poisson–Boltzmann equations, of which the data is not so smooth.