Publications

Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials

2016:

P. Hennig, M. Kästner, P. Morgenstern, D. Peterseim.
Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. Computer Methods in Applied Mechanics and Engineering, 2016.

P. Morgenstern.
Globally structured three-dimensional analysis-suitable t- splines: Definition, linear independence and m-graded local refinement.
SIAM Journal on Numerical Analysis, 2016.

M. Kästner, P. Hennig, T. Linse, V. Ulbricht.
Phase-field modelling of damage and fracture – convergence and local mesh refinement.
In: K. Naumenko and M. Assmus (Eds.), Advanced Methods of Continuum Mechanics for Materials and Structures, 2016.

D. Peterseim.
Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors.
In: G.R. Barrenechea, F. Brezzi, A. Cangiani, E.H. Georgoulis (Eds.), Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, 2016.

A. Buffa, C. Giannelli, P. Morgenstern, D. Peterseim.
Complexity of hierarchical refinement for a class of admissible mesh configurations.
Computer Aided Geometric Design, 2016.

P. Hennig, S. Müller, M. Kästner.
Bézier extraction and adaptive refinement of truncated hierarchical NURBS.
Computer Methods in Applied Mechanics and Engineering, 2016.

C. Carstensen, D. Peterseim, A. Schröder.
The norm of a discretized gradient in H(div)∗ for a posteriori finite element error analysis.
Numerische Mathematik, 2016.

2015:

P. Morgenstern, D. Peterseim.
Analysis-suitable adaptive T-mesh refinement with linear complexity.
Computer Aided Geometric Design, 2015.

Finite element approximation of functions of bounded variation and application to models of damage, fracture and plasticity

2017:

S. Bartels, M. Milicevic.
Alternating direction method of multipliers with variable step sizes.
Preprint, 2017

2016:

S. Bartels, M. Milicevic.
Iterative solution of a constrained total variation regularized model problem.
Discrete and Continuous Dynamical Systems, 2016.

S. Bartels.
Broken Sobolev space iteration for total variation regularized minimization problems.
IMA Journal of Numerical Analysis, 2016.

S. Bartels, M. Milicevic.
Stability and experimental comparison of prototypical iterative schemes for total variation regularized problems.
Computational Methods in Applied Mathematics, 2016.

2015:

S. Bartels, R. H. Nochetto, A. J. Salgado.
A total variation diminishing interpolation operator and applications.
Mathematics of Computation, Vol. 84,  2015.

S. Bartels.
Error control and adaptivity for a variational model problem defined on functions of bounded variation.
Mathematics of Computation, Vol. 84, 2015.

S. Bartels.
Numerical methods for nonlinear partial differential equations.
Springer Series in Computational Mathematics, Vol. 47, Springer, 2015.

High-order immersed-boundary methods in solid mechanics for structures generated by additive processes

2016:

C. Carstensen, D. Peterseim, A. Schröder.
The norm of a discretized gradient in H(div)∗ for a posteriori finite element error analysis.
Numerische Mathematik, 2016.

L. Kudela, N. Zander, T. Bog, S. Kollmannsberger, E. Rank.
Smart octrees: Accurately integrating discontinuous functions in 3D.
Comput. Methods Appl. Mech. Engrg., 2016

M. Joulaian, S. Hubrich, A. Düster.
Numerical integration of discontinuities on arbitrary domains based on moment fitting.
Computational Mechanics, 2016.

N. Zander, T. Bog, M. Elhaddad, F. Frischmann, S. Kollmannsberger, E. Rank.
The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes.
Comput. Methods Appl. Mech. Engrg, 2016.

N. Zander, M. Ruess, T. Bog, S. Kollmannsberger, E. Rank.
Multi-Level hp- Adaptivity for Cohesive Fracture Modelling.
International Journal for Numerical Methods in Engineering, 2016.

P. Di Stolfo, A. Schröder, N. Zander, S. Kollmannsberger.
An easy treatment of hanging nodes in hp-finite elements.
Finite Elements in Analysis and Design, 2016.

2015:

N. Zander, T. Bog, S. Kollmannsberger, D. Schillinger, E. Rank.
Multilevel hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes.
Computational Mechanics, 2015.

A. Rademacher, A. Schröder.
Dual Weighted Residual Error Control for Frictional Contact Problems.
Computational Methods in Applied Mathematics, 2015

Hybrid discontinuous Galerkin methods in solid mechanics

2016:

A. Seitz, P. Farrah, J. Kremheller, B. Wohlmuth, W. Wall, A. Popp.
Isogeometric dual mortar methods for computational contact mechanics.
Computer Methods in Applied Mechanics and Engineering, 2016.

2015:

E. Brivadis, A. Buffa, B. Wohlmuth, L. Wunderlich.
The Influence of Quadrature Errors on Isogeometric Mortar Methods.
Isogeometric Analysis and Applications 2014. Springer, 2015.

E. Brivadis, A. Buffa, B. Wohlmuth, L. Wunderlich.
Isogeometric mortar methods.
Computer Methods in Applied Mechanics and Engineering, 2015.

O. Steinbach, B. Wohlmuth, L.Wunderlich.
Trace and flux a priori error estimates in finite element approximations of Signorini-type problems.
IMA Journal of Numerical Analysis, 2015.

Novel finite element technologies for anisotropic media

2017:

J. Schröder, N. Viebahn, P. Wriggers, F. Auricchio, K. Steeger.
On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations. accepted for publication in Computational Mechanics 2017.

P. Wriggers, B. D. Reddy, W. Rust, B. Hudobivnik.
Efficient virtual element formulations for compressible and incompressible finite deformations. Computational Mechanics, DOI: 10.1007/s00466-017-1405-4, 2017

P. Wriggers, B. Hudobivnik, J. Schröder.
Finite and virtual element formulations for large strain anisotropic material with inextensive fibers, in Multiscale Modeling of Heterogeneous Structures, eds. J. Soric and P. Wriggers, Lecture Notes in Applied and Computational Mechanics, Springer, 2017.

 

 

2016:

N. Viebahn, P.M. Pimenta, J. Schröder.
A Simple triangular finite element for nonlinear thin shells - Statics, Dynamics and Anisotropy. Computational Mechanics, DOI: 10.1007/s00466-016-1343-6, 2016

J. Schröder, N. Viebahn, D. Balzani, P. Wriggers.
A novel mixed finite element for finite anisotropic elasticity; the SKA-element Simplified Kinematics for Anisotropy.
Computer Methods in Applied Mechanics and Engineering, 2016.

P. Wriggers, J. Schröder, F. Auricchio.
Finite element formulations for large strain anisotropic material with inextensive fibers.
Advanced Modeling and Simulation in Engineering Sciences, 2016.

Large-scale simulation of pneumatic and hydraulic fracture with a phase-field approach

2017:

C. Hesch, A. J. Gil, R. Ortigosa, M. Dittmann, C. Bilgen, P. Betsch, M. Franke, A. Janz, K. Weinberg.
A framework for polyconvex large strain phase-field methods to fracture.
Comput. Methods Appl. Mech. Engrg., 2017.

2016:

C. Hesch, S. Schuß, M. Dittmann, M. Franke and K. Weinberg.
Isogeometric analysis and hierarchical refinement for higher-order phase-field models.
Comput. Methods Appl. Mech. Engrg, 2016.

C. Hesch, M. Franke, M. Dittmann and I. Temizer.
Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems.
Comput. Methods Appl. Mech. Engrg, 2016

K. Weinberg, T. Dally, S. Schuß, M. Werner and C. Bilgen.
Modeling and numerical simulation of crack growth and damage with a phase-field approach. GAMM-Mitteilungen, 2016.