Weighted residual estimators for a posteriori estimation of pointwise gradient errors in quasilinear elliptic problems

We present a weighted residual scheme for estimation of pointwise gradient errors in finite element methods for quasilinear elliptic problems. First we define computable residual weights which may be conveniently determined using local ellipticity properties of the underlying differential operator. Using a combination of theoretical and computational results, the resulting a posteriori error estimator is shown to bound the error up to nonessential constants and higher-order terms. Further properties of this estimator are investigated and illustrated using computational experiments.