A posteriori error estimates for nonlinear problems. Lr -estimates for finite element discretizations of elliptic equations

Abstract

We extend the general framework of [18] for deriving a posteriori error estimates for approximate solutions of nonlinear elliptic problems such that it also yields Lr-error estimates. The general results are applied to finite element discretizations of scalar quasilinear elliptic pdes of 2nd order and the stationary incompressible Navier-Stokes equations. They immediately yield a posteriori error estimates for an Lr-norm of the error which can easily be computed from the given data of the problem and the computed numerical solution and which give globed upper and local lower bounds on the error of the numerical solution © Elsevier, Paris.