Stabilized finite element schemes with LBB-stable elements for incompressible flows

AbstractWe study stabilized FE approximations of SUPG type to the incompressible Navier–Stokes problem. Revisiting the analysis for the linearized model, we show that for conforming LBB-stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal-order approximation. Then we analyze a reduced SUPG scheme often used in practice for LBB-stable elements. To provide the reduced scheme with appropriate stability estimates we introduce a modified LBB condition which is proved for a family of FE approximations. The analysis is given for the linearized equations. Numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

Benzodiazepines in the Management of Seizures and Status Epilepticus: A Review of Routes of Delivery, Pharmacokinetics, Efficacy, and Tolerability.

Status epilepticus (SE) is an acute, life-threatening medical condition that requires immediate, effective therapy. Therefore, the acute care of prolonged seizures and SE is a constant challenge for healthcare professionals, in both the pre-hospital and the in-hospital settings. Benzodiazepines (BZDs) are the first-line treatment for SE worldwide due to their efficacy, tolerability, and rapid onset of action. Although all BZDs act as allosteric modulators at the inhibitory gamma-aminobutyric acid (GABA) <sub>A</sub> receptor, the individual agents have different efficacy profiles and pharmacokinetic and pharmacodynamic properties, some of which differ significantly. The conventional BZDs clonazepam, diazepam, lorazepam and midazolam differ mainly in their durations of action and available routes of administration. In addition to the common intravenous, intramuscular and rectal administrations that have long been established in the acute treatment of SE, other administration routes for BZDs-such as intranasal administration-have been developed in recent years, with some preparations already commercially available. Most recently, the intrapulmonary administration of BZDs via an inhaler has been investigated. This narrative review provides an overview of the current knowledge on the efficacy and tolerability of different BZDs, with a focus on different routes of administration and therapeutic specificities for different patient groups, and offers an outlook on potential future drug developments for the treatment of prolonged seizures and SE