Working group: Prof. R. Kornhuber (Numerical Analysis of Partial Differential Equations)

2015/10–present: Fighting cancer.

2015: Postdoc, FU Berlin, Germany

2011-2014: PhD^{1,2} in mathematics, FU Berlin, Germany

2006-2010: Diploma in mathematics, FU Berlin, Germany

2006: University-entrance diploma, Herder-Gymnasium Berlin, Germany

Member of the Berlin Mathematical School.

^{1} Supported through a 1-year scholarship by the (FU Berlin) Center for Scientific Simulation (2011).

^{2} Supported through a 3-year scholarship by the Helmholtz graduate research school GeoSim (2012-2014).

Supplement to "Analogue earthquakes and seismic cycles: Experimental modelling across timescales"

M. Rosenau, F. Corbi, S. Dominguez, M. Rudolf, M. Ritter, E. Pipping

GFZ Data Services (2016)My contribution consists of the video NumEQ.mp4 in group A. For the 2D problem that was numerically solved in the 2016 Geophys. J. Int. publication (see below) it shows the velocity field in the upper plate across multiple seismic cycles.

The distribution of the arrows representing the vector field is optimized for visual clarity (in particular, it is uniform) and different from the (non-uniform) spatial resolution of the numerical simulation.

On the efficient and reliable numerical solution of rate-and-state friction problems

E. Pipping, R. Kornhuber, M. Rosenau, and O. Oncken

Geophys. J. Int. 204.3 (2016) 1858–1866

Free fallback access: Peer-reviewed version accepted for publicationAn excerpt from my dissertation, focussed on applications: A mathematical problem is presented but not derived and not analysed. The algorithm is only hinted at, not presented in detail. Results presented here constitute an improvement over those from my dissertation in that: (1) they also cover a 3D setting and (2) they were obtained after a bug was fixed (see below).

Dynamic problems of rate-and-state friction in viscoelasticity

E. Pipping (supervisor: R. Kornhuber)

Dissertation (2014)Derives a mathematical problem from the geophysical setting of a viscoelastic body undergoing infinitesimal strain while sliding on top of a rigid foundation, subject to rate-and-state friction. The problem is analysed, an algorithm is presented and convergence is proved in a semi-discrete setting. 2D simulation results are obtained, interpreted, and compared to laboratory measurements.

A small bug in the numerical code has been discovered since the publication; it caused the prescribed normal stress to be exaggerated by a factor of two, so that it equalled twice the lithospheric normal stress. This needs to be taken into account when interpreting the simulation results. The 2016 publication contains results where this bug has been fixed.

Variational formulation of rate- and state-dependent friction problems

E. Pipping, O. Sander, and R. Kornhuber

Z. angew. Math. Mech. 95.4 (2013/2015) 377–395

Free fallback access: Peer-reviewed version accepted for publicationAn early attempt to analyse and solve the mathematical problems arising from an elastic body undergoing infinitesimal strain while sliding on top of a rigid foundation, subject to rate-and-state friction. The approach and results are suboptimal, the presentation is difficult to follow. The reader is, therefore, referred to one of the later publications on the subject, since they supersede this work in every way.

- L- and M-structure in lush spaces

E. Pipping

Zh. Mat. Fiz. Anal. Geom. 7.1 (2011) 87–95

The lushness property of a Banach space is shown to be inherited by certain subspaces, namely L-summands and M-ideals. Lush spaces thus behave the same way as almost-CL spaces and spaces of numerical index one in this respect.

2015-07-01: (Conference) SIAM Geosciences 2015 Slides

2014-12-10: (PhD defence) Disputation slides: part I, part II

2013-11-28: (Workshop) BMS Intensive Course on Evolution Equations Slides

2013-06-19: (Conference) SIAM Geosciences 2013 Slides

2012-07-15: (Conference) GeoMod Poster Abstract

2010-04-06: (Diploma) Thesis (German)

Email: elias.pipping@fu-berlin.de