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Representation of equilibrium solutions to the table problem of growing sandpiles

Piermarco Cannarsa, Pierre Cardaliaguet (2004)

Journal of the European Mathematical Society

In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain Ω 2 . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...

Residual based a posteriori error estimators for eddy current computation

Rudi Beck, Ralf Hiptmair, Ronald H.W. Hoppe, Barbara Wohlmuth (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider H(curl;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. Under certain assumptions on material parameters and computational domains, we derive local lower bounds and a global upper bound for the total error measured in...

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