Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II

This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. For 1<p<2 the bilinear form of the boundary element method fails to be continuous in natural function spaces associated to the nonlinear operator. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. The a posteriori estimate complements recent estimates obtained for mixed finite element formulations of friction problems in linear elasticity.Comment: 20 pages, corrected typos and improved expositio

A Nash-Hormander iteration and boundary elements for the Molodensky problem

We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash-Hormander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral. A boundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.Comment: 32 pages, 14 figures, to appear in Numerische Mathemati

Roche volume filling and the dissolution of open star clusters

From direct N-body simulations we find that the dynamical evolution of star clusters is strongly influenced by the Roche volume filling factor. We present a parameter study of the dissolution of open star clusters with different Roche volume filling factors and different particle numbers. We study both Roche volume underfilling and overfilling models and compare with the Roche volume filling case. We find that in the Roche volume overfilling limit of our simulations two-body relaxation is no longer the dominant dissolution mechanism but the changing cluster potential. We call this mechnism "mass-loss driven dissolution" in contrast to "two-body relaxation driven dissolution" which occurs in the Roche volume underfilling regime. We have measured scaling exponents of the dissolution time with the two-body relaxation time. In this experimental study we find a decreasing scaling exponent with increasing Roche volume filling factor. The evolution of the escaper number in the Roche volume overfilling limit can be described by a log-logistic differential equation. We report the finding of a resonance condition which may play a role for the evolution of star clusters and may be calibrated by the main periodic orbit in the large island of retrograde quasiperiodic orbits in the Poincar\'e surfaces of section. We also report on the existence of a stability curve which may be of relevance with respect to the structure of star clusters.Comment: 14 pages, 10+1 figures, accepted by Astronomische Nachrichte

Numerical simulations of the nonlinear Molodensky problem

We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. Our solution procedure solves a sequence of exterior oblique Robin problems and is based on a Nash-H\"{o}rmander iteration. We apply smoothing with the heat equation to overcome a loss of derivatives in the surface update. Numerical results compare the error between the approximation and the exact solution in a model problem.Comment: 13 pages, submitted to the proceedings of the European Geosciences Union General Assembly 2013 / Studia geophysica et geodaetic