German Priority Programme 1748 (DFG SPP 1748) Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis

Numerical simulation techniques are an essential component for the construction, design and optimisation of cutting-edge technologies as for example innovative products, new materials as well as medical-technical applications and production processes. These important developments pose great demands on quality, reliability and capability of numerical methods, which are used for the simulation of these complex problems. Challenges are for example capture of incompressibility, anisotropy and discontinuities. Existing computer-based solution methods often provide approximations which cannot guarantee substantial, absolutely necessary stability criteria respectively fulfill them. Especially in the field of geometrical and material non-linearity such uncertainties appear. Typical problems are insufficient or even pathological stress approximations due to unsuitable approximation spaces as well as weak convergence behaviour because of stiffening effects or mesh distortion. Similar problems arise in the framework of crack and contact problems. Here the resolution of the local discontinuities as well as their evolution plays a key role. The scientists of the SPP 1748 have set themselves the goal to establish a new quality in the area of non-conventional discretisation methods. Herein the work programme of the SPP is founded:

1. The evolution of modern non-conventional discretisation methods,
2. their mathematical analysis and
3. the exploration of their application limits on the basis of suitable benchmark problems

Bad Honnef

Annual Meeting 2019


The fourth annual meeting of the SPP 1748 took place at the Physikzentrum Bad Honnef at the end of June and start of July 2019. More information to the meeting can be found here


Bad Honnef

Annual Meeting 2017


The third annual meeting of the SPP 1748 took place at the Physikzentrum Bad Honnef at the end of August 2017. More information to the meeting can be found here


Pavia, Collegio Borromeo

Annual Meeting 2016


The second annual meeting of the SPP 1748 took place at the Collegio Borromeo in Pavia at the end of August. Beside the presentations, where each subproject presented the progress of the momentary year, the more than 40 participants had the privilige to listen to the plenary session given by Prof. Ferdinando Auricchio.
More information to the meeting can be found here


ECCOMAS-Congress 2016 MS 923 - Novel Discretization Methods – Mathematical and Mechanical Aspects

Jörg Schröder (University of Duisburg-Essen, Germany)
Peter Wriggers (Leibniz Universität Hannover, Germany)
Ferdinando Auricchio (University of Pavia, Italy)
Carsten Carstensen (Humbolt-Universität zu Berlin, Germany)

The great success of practical computational engineering for advanced
problems in solid mechanics stimulates the ongoing research in this
emerging area. However, only a few partial mathematical convergence
proofs and stability/robustness studies exist in this challenging field.
Consequently many fundamental questions related to reliable and
effective numerical simulations in nonlinear mechanics are still open.

The success of mixed finite element formulations in linear elasticity
with focus on the accuracy of the stress variable motivates new research
leading to novel discretization schemes. This and recent surprising
advantages of related nonconforming finite element methods in nonlinear
partial differential equations with guaranteed lower eigenvalue bounds
or lower energy bounds in convex minimization problems suggest the
investigation of mixed and simpler generalized mixed finite element
methods such as discontinuous Petrov-Galerkin schemes for linear
elasticity as well as for nonlinear elasticity based on isotropic and
anisotropic polyconvex energy densities.

Combinations of least-squares finite element methods with those of
hybridized methods recently led to discontinuous Petrov Galerkin (dPG)
FEMs. They minimize a residual inherited from a piecewise ultra weak
formulation in a non-standard localized dual norm.

However, there exist many other emerging new schemes which lead to
progress in reliable and robust applications of finite element methods
to complex engineering problems. The minisymposium is open to new ideas
and schemes that describe non-standard numerical methods for solutions
in solid mechanics.

ECCOMAS-Congress 2016 MS 904 - Advanced Minimal Residual Discretization

Carsten Carstensen (Humbolt-Universität zu Berlin, Germany)
Dietmar Gallistl (Universität Bonn, Germany)

The mathematical foundation of minimal residual methods and their application in engineerings and sciences is an emerging area of computational mathematics and scientific computing. It consists of the least squares finite element methods as well as the discontinuous Petrov Galerkin methods which may be seen as mixed generalized finite element methods. Amongst the advantages of those schemes are instant stability and built-in a posteriori error control.

We enjoyed eight very interesting presentations by young scientists with an average age of 27. The topics of the minisymposium ranged from adaptive mesh-refinement and complexity considerations to implementation aspects and preconditioning.

Coding Week - Technische Universität München

Workshop on Isogeometric Finite Element Data Structures based on Bézier Extraction

14.-18. March, 2016 at the Technische Universität München

Img 1860

As part of the DFG Priority Project SPP1748 a coding week on Isogeometric Finite Element Data Structures based on Bézier Extraction was intended for the doctoral candidates at the Technische Universität München.

More information can be found here.

TU - Hamburg Harburg

Annual Meeting 2015


von Martina Brinkmann, TUHH


The first annual meeting of the SPP 1748 taked place at the TU Hamburg-Harburg at the end of august. More than 30 researcher joined the two-day meeting in order to present their progress. Additional to the presentations of the projects, the discussions and conversations, a joint dinner directly at the port of Hamburg rounded out the event.
More information to the meeting can be found here


Prof. Dr.-Ing. habil J. Schröder,
Universität Duisburg Essen (Coordinator) link

Prof. Dr. rer. nat. habil. C. Carstensen,
Humboldt-Universität zu Berlin (Vice-Coordinator) link

Prof. Dr.-Ing. habil. S. Reese,
RWTH Aachen link

Prof. Dr. rer. nat. habil. G. Starke,
Universität Duisburg Essen link

Prof. Dr.-Ing. habil. P. Wriggers,
Leibniz Universität Hannover link

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