On maximum norm convergence of multigrid methods for two-point boundary value problems

Multigrid methods applied to standard linear finite element discretizations of linear elliptic two-point boundary value problems are considered. In the multigrid method damped Jacobi or damped Gauss–Seidel is used as a smoother. It is shown that the contraction number with respect to the maximum norm has an upper bound which is smaller than one and independent of the mesh size

On maximum norm convergence of multigrid methods for two-point boundary value problems

Multigrid methods applied to standard linear finite element discretizations of linear elliptic two-point boundary value problems are considered. In the multigrid method damped Jacobi or damped Gauss–Seidel is used as a smoother. It is shown that the contraction number with respect to the maximum norm has an upper bound which is smaller than one and independent of the mesh size

On maximum norm convergence of multigrid methods for elliptic boundary value problems

Multigrid methods applied to standard linear finite element discretizations of linear elliptic boundary value problems in two dimensions are considered. In the multigrid method, damped Jacobi or damped Gauss-Seidel is used as a smoother. It is proven that the two-grid method with v pre-smoothing interations has a contraction number with respect to the maximum norm that is (asymptotically) bounded by Cv-1/2|lnhk|2, with hk a suitable mesh size parameter. Moreover, it is shown that this bound is sharp in the sense that a factor |ln hk| is necessary

Zika virus infection in 18 travellers returning from Surinam and the Dominican Republic, The Netherlands, November 2015–March 2016

Purpose: We report 18 cases of confirmed Zika virus (ZIKV) infection in travellers returning to the Netherlands from Surinam (South America, bordering northern Brazil) and the Dominican Republic. Methods: In a multi-centre study, we collected epidemiological, virological and clinical characteristics, as well as data on travel history, underlying illness and laboratory results of the 18 imported ZIKV infection cases using a standardised form. Results: Most cases had a self-limiting course of disease, two patients developed complications, one had Guillain–Barré and another had severe thrombocytopenia. Four patients had underlying illness. One of the reported cases was pregnant. Three of 13 patients tested had a weak-positive result for dengue IgM. The majority of patients were born in Suriname and/or visiting friends and relatives (VFR). Conclusions: Providing pre-travel advice among travellers, especially VFR travellers, is needed to enhance the use of preventive measures against ZIKV infection. Further evidence on health risks associated with ZIKV infection is urgently needed