Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator (Q2372322)

The paper is concerned with the study of the efficiency and reliability of a residual based anisotropic error estimator for the Poisson problem with mixed boundary conditions in \({\mathbb R}^2\). The proposed estimator combines anisotropic estimates of the interpolation error for linear triangular finite elements and the Zienkiewicz-Zhu procedure to recover the gradient of the exact solution. This anisotropic error estimator can be used to derive an adaptive procedure used to obtain a numerical solution satisfying a given accuracy. The algorithm is validated on some numerical test cases.