Pointwise a posteriori error estimates for monotone semi-linear equations (Q2433992)

A continuous barrier function \(w\) is determined such that the solution of the continuous problem lies between \(u_h-w\) and \(u_h+w\). Negative norms of the residues are estimated and the continuous maximum principle is applied. The technique that has been used by \textit{R. H. Nochetto, K. G. Siebert} and \textit{A. Veeser} [ibid. 95, No.~1, 163--195 (2003; Zbl 1027.65089); SIAM J. Numer. Anal. 42, No.~5, 2118--2135 (2005; Zbl 1095.65099)] to linear problems, is extended here to monotone semi-linear equations. Numerical experiments illustrate reliability and efficiency properties of the corresponding estimators and investigate the performance of the resulting adaptive algorithms in terms of the polynomial order and quadrature.