Optic Nerve Head Change in Non-Arteritic Anterior Ischemic Optic Neuropathy and Its Influence on Visual Outcome

To evaluate changes in cup/disc (C/D) diameter ratios and parapapillary atrophy in patients with non-arteritic anterior ischemic optic neuropathy (NA-AION), using morphometric methods.The clinical non-interventional study included 157 patients with unilateral or bilateral NA-AION. Optic disc photographs taken from both eyes at the end of follow-up were morphometrically examined.Follow-up was 86.3±70.3 months. Horizontal and vertical disc diameters (P = 0.30;P = 0.61, respectively), horizontal and vertical C/D ratios (P = 0.47;P = 0.19,resp.), and size of alpha zone and beta zone of parapapillary atrophy (P = 0.27;P = 0.32,resp.) did not differ significantly between affected eyes and contralateral normal eyes in patients with unilateral NA-AION. Similarly, horizontal and vertical disc diameters, horizontal and vertical C/D ratios, and size of alpha zone and beta zone did not vary significantly (all P>0.05) between the unaffected eyes of patients with unilateral NA-AION and the eyes of patients with bilateral NA-AION. Optic disc diameters, C/D ratios, size of alpha zone or beta zone of parapapillary atrophy were not significantly associated with final visual outcome in the eyes affected with NA-AION (all P>0.20) nor with the difference in final visual acuity between affected eyes and unaffected eyes in patients with unilateral NA-AION (all P>0.25).NA-AION did not affect C/D ratios nor alpha zone and beta zone of parapapillary atrophy. Optic disc size was not related to the final visual acuity outcome in NA-AION

A posteriori error control and adaptivity for Crank-Nicolson finite element approximations for the linear Schrödinger equation

We derive optimal order a posteriori error estimates for fully discrete approximations of linear Schrödinger-type equations, in the L∞ (L2)-norm. For the discretization in time we use the Crank–Nicolson method, while for the space discretization we use finite element spaces that are allowed to change in time. The derivation of the estimators is based on a novel elliptic reconstruction that leads to estimates which reflect the physical properties of Schrödinger equations. The final estimates are obtained using energy techniques and residual-type estimators. Various numerical experiments for the one-dimensional linear Schrödinger equation in the semiclassical regime, verify and complement our theoretical results. The numerical implementations are performed with both uniform partitions and adaptivity in time and space. For adaptivity, we further develop and analyze an existing time-space adaptive algorithm to the cases of Schrödinger equations. The adaptive algorithm reduces the computational cost substantially and provides efficient error control for the solution and the observables of the problem, especially for small values of the Planck constant.</p