Zusammenfassung: FiJr die StraBenverkehrsplanung m6chte man den VerkehrsfluB auf den einzelnen StraSen des Netzes absch~itzen, wenn die Zahl der Fahrzeuge bekannt ist, die zwischen den einzelnen Punkten des StraBennetzes verkehren. Welche Wege am gtinstigsten sind, hiingt nun nicht nur vonder Beschaffenheit der Stral3e ab, sondern auch vonder Verkehrsdichte. Es ergeben sich nicht immer optimale Fahrzeiten, wenn jeder Fahrer nur ftir sich den gtinstigsten Weg heraussucht. In einigen Fiillen kann sich durch Erweiterung des Netzes der VerkehrsfluB sogar so umlagern, dab gr6Bere Fahrzeiten erforderlich werden.
Summary:For each point of a road network let be given the number of cars starting from it, and the destination of the cars. Under these conditions one wishes to estimate the distribution of the traffic flow. Whether a street is preferable to another one depends not only upon the quality of the road but also upon the density of the flow. If every driver takes that path which looks most favorable to him, the resultant running times need not be minimal. Furthermore it is indicated by an example that an extension of the road network may cause a redistribution of the traffic which results in longer individual running times.
F or each point of a road network, let there be given the number of cars starting from it, and the destination of the cars. Under these conditions one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favorable to him, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times.
Abstract. Reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem. A cheap computation of such functions via equilibration is well known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to the curl-curl equation and edge elements. The construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions. For this reason, Raviart-Thomas elements are extended in the spirit of distributions.
Equilibrated residual error estimators applied to high order finite elements are analyzed. The estimators provide always a true upper bound for the energy error. We prove that also the efficiency estimate is robust with respect to the polynomial degrees. The result is complete for tensor product elements. In the case of simplicial elements, the theorem is based on a conjecture, for which numerical evidence is provided.
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