A posteriori error analysis of an augmented mixed finite element method for Darcy flow

We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual-mixed approach suitable residual type terms arising from Darcy's law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple a posteriori error estimator and prove that it is reliable and locally efficient. Finally, we provide several numerical experiments that illustrate the theoretical results and support the use of the corresponding adaptive algorithm in practice

Rey–Osterrieth Complex Figure – copy and immediate recall (3 minutes): Normative data for Spanish-speaking pediatric populations

OBJECTIVE: To generate normative data for the Rey–Osterrieth Complex Figure (ROCF) in Spanish-speaking pediatric populations. METHOD: The sample consisted of 4,373 healthy children from nine countries in Latin America (Chile, Cuba, Ecuador, Guatemala, Honduras, Mexico, Paraguay, Peru, and Puerto Rico) and Spain. Each participant was administered the ROCF as part of a larger neuropsychological battery. The ROCF copy and immediate recall (3 minutes) scores were normed using multiple linear regressions and standard deviations of residual values. Age, age2, sex, and mean level of parental education (MLPE) were included as predictors in the analyses. RESULTS: The final multiple linear regression models showed main effect for age on copy and immediate recall scores, such that scores increased linearly as a function of age. Age2 affected ROCF copy score for all countries, except Puerto Rico; and ROCF immediate recall scores for all countries, except Chile, Guatemala, Honduras, Paraguay, and Puerto Rico. Models indicated that children whose parent(s) had a MLPE >12 years obtained higher scores compared to children whose parent(s) had a MLPE≤12 years for Chile, Puerto Rico, and Spain in the ROCF copy, and Paraguay and Spain for the ROCF immediate recall. Sex affected ROCF copy and immediate recall score for Chile and Puerto Rico with girls scoring higher than boys. CONCLUSIONS: This is the largest Spanish-speaking pediatric normative study in the world, and it will allow neuropsychologists from these countries to have a more accurate approach to interpret the ROCF Test in pediatric populations

Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity. Dedicated to Professor Rodolfo Rodríguez on the occasion of his 60th birthday.

We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency bound. Numerical experiments illustrate the performance of the corresponding adaptive algorithms and support the theoretical results

Multi-messenger Observations of a Binary Neutron Star Merger

International audienceOn 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\sim 1.7\,{\rm{s}}$ with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg(2) at a luminosity distance of ${40}_{-8}^{+8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 $\,{M}_{\odot }$. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\sim 40\,{\rm{Mpc}}$) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ∼10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position $\sim 9$ and $\sim 16$ days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta