We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computational times are typically reduced by several orders of magnitude

In an effort to contain the spread of COVID-19, Germany has gradually implemented mobility restrictions culminating in a partial lockdown and contact restrictions on 22 March. The easing of the restrictions began 1 month later, on 20 April. Analysis of the consequences of these measures for mobility and infection incidence is of public health interest. A dynamic cohort of about 2,000 individuals in Germany aged 16–89 years provided individual information on demographic variables, and their continuous geolocation via a smartphone app. Using interrupted time series analysis, we investigated mobility by age, sex, and previous mobility habits from 13 January until 17 May 2020, measured as median daily distance traveled before and after restrictions were introduced. Furthermore, we have investigated the association of mobility with the number of new cases and the reproduction number. Median daily distance traveled decreased substantially in total and homogeneously across all subgroups considered. The decrease was strongest in the last week of March followed by a slight increase. Relative reduction of mobility developed parallel with number of new cases and the daily estimated reproduction number in the weeks after contact restrictions were implemented. The increase in mobility from mid-April onwards, however, did not result in increased case numbers but in further decrease. Other behavioral changes, e.g., wearing masks, individual distancing, or general awareness of the COVID-19 hazards may have contributed to the observed further reduction in case numbers and constant reproduction numbers below one until mid-July.

We consider the problem of solving numerically the stationary incompressible Navier-Stokes equations in an exterior domain in two dimensions. For numerical purposes we truncate the domain to a …nite sub-domain, which leads to the problem of …nding so called "arti…cial boundary conditions" to replace the boundary conditions at in…nity. To solve this problem we construct -by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of Goldstein and Van Dyke -a smooth divergence free vector …eld depending explicitly on drag and lift and describing the solution to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to nonsymmetric ‡ows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent way as an integral part of the solution process. When compared with our previous paper where …rst order asymptotic expressions were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost for determining lift and drag to a given precision by typically another order of magnitude.Mathematics Subject Classi…cation (2000). 76D05, 76D25, 76M10, 41A60, 35Q35.

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Abstract. An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information about it. The approach and the state of the art of the information service are described here.