# Publications

## Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials

## 2017:

D. Peterseim, M. Schedensack.

*Relaxing the CFL condition for the wave equation on adaptive meshes.*

J. Sci. Comput., pages 1–18, 2017.

D. Gallistl, P. Huber, D. Peterseim.

*On the stability of Raleigh- Ritz method for eigenvalues.*

Numerische Mathematik, pages 1–13, 2017.

P. Morgenstern.

*Mesh Refinement Strategies for the Adaptive Isogeometric Method. PhD thesis.*

Rheinische Friedrich-Wilhelms-Universität Bonn, 2017.

T. Linse, P. Hennig, M. Kästner, R. De Borst.

*An analysis of convergence in phase-field models for brittle fracture.*

submitted to: International Journal of Solids and Structures, 2017.

A. C. Hansen-Dörr, P. Hennig, M. Kästner, K. Weinberg.

*A numerical analysis of the fracture toughness in phase-field modelling of adhesive*

fracture.

submitted to: Proceedings in Applied Mathematics and Mechanics.

## 2016:

D. Gallistl, D. Peterseim.

*Computation of quasilocal effective diffusion tensors and connections to the mathematical theory of homogenization.*

Multiscale Modeling and Simulation , 2016.

D. Gallistl, D. Peterseim, C. Carstensen.

*Multiscale petrov-galerkin fem for acoustic scattering.*

Proceedings in Applied Mathematics an Mechanics, 2016.

P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn.

*Towards adaptive discontinuous petrov-galerkin methods.*

Proceedings in Applied Mathematics an Mechanics, 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:

R. Rossi, M. Thomas.

From nonlinear to linear elasticity in a coupled rate-dependent/rate-independent system for brittle

delamination.

Accepted in INDAM-Springer series: Symposium on Trends in Applications of Mathematics to Mechanics, 2017.

S. Bartels, M. Milicevic.

*Alternating direction method of multipliers with variable step sizes.*

Preprint, 2017

S. Bartels, M. Milicevic, M. Thomas.

*Numerical approach to a model for quasistatic damage with spatial BV-regularization.*

Preprint, 2017.

R. Rossi, M. Thomas.

*From adhesive to brittle delamination in visco-elastodynamics.*

Accepted in M3AS, Preprint, 2017.

R. Rossi, M. Thomas.

*Coupling rate-independent and rate-dependent processes: Existence results.*

Accepted in SIMA, Preprint, 2017.

M. Thomas, C. Zanini.

*Cohesive zone-type delamination in visco-elasticity.*

Accepted in DCDS-S, 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.

## Foundation and Application of Generalized Mixed FEM Towards Nonlinear Problems in Solid Mechanics

## 2017:

C. Carstensen, P. Bringmann, F. Hellwig, P. Wriggers.

*Nonlinear discontinuous Petrov-Galerkin methods.*

Submitted, 2017.

C. Carstensen, D. Gallistl, J. Gedicke.

*Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM.*

Submitted, 2017.

C. Carstensen, F. Hellwig.

*Constants in Discrete Poincaré and Friedrichs Inequalities and Discrete Quasi-Interpolation.*

Submitted, 2017.

C. Carstensen, D. Liu, J. Alberty.

*Convergence of dG(1) in elastoplastic evolution.*

Submitted, 2017.

C. Carstensen, J. Storn.

*Asymptotic exactness of the least-squares finite element residual.*

Submitted, 2017.

P. Bringmann, C. Carstensen.

*An adaptive least-squares FEM for the Stokes equations with optimal convergence rates.*

Numer. Math., 2017.

P. Bringmann, C. Carstensen.

*h-adaptive least-squares finite element method for the 2d stokes equations of any order with optimal*

convergence rates.

Comput. Math. Appl., 2017.

P. Bringmann, C. Carstensen, E. J. Park.

*Convergence of natural adaptive least squares finite element methods.*

Numer. Math., 2017.

## 2016:

C. Carstensen, S. Puttkammer.

*A low-order discontinuous Petrov-Galerkin method for the Stokes equations.*

Submitted, 2016.

C. Carstensen, H. Rabus.

*Axioms of adaptivity for separate marking.*

Resubmitted to: SINUM, 2016.

P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn.

*Towards adaptive discontinuous Petrov-Galerkin methods.*

Proc. Appl. Math. Mech., 2016.

C. Carstensen, L. Demkowicz, J. Gopalakrishnan.

*Breaking spaces and forms for the DPG method and applications including Maxwell equations.*

Comput. Math. Appl., 2016.

C. Carstensen, F. Hellwig.

*Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity.*

SIAM J. Numer. Anal., 2016.

C. Carstensen, D. Peterseim, A. Schröder.

*The norm of a discretized gradient in H(div)* for a posteriori finite element error analysis.*

Numer. Math., 2016.

T. Steiner, P. Wriggers, S. Löhnert.

*A discontinuous Galerkin finite element method for linear elasticity using a mixed integration scheme to circumvent shear-locking.*

Proc. Appl. Math. Mech., 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.

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

## 2017:

A. Düster, E. Rank, B. Szabo.

*The p-Version of the Finite Element and Finite Cell Methods.*

Encyclopedia of Computational Mechanics, volume 2, pages 1–35, 2017.

S. Kollmannsberger, A. Özcan, M.Carraturo, N. Zander, E. Rank.

*A hierarchical computational model for moving thermal loads and phase changes with applications to Selective Laser Melting.*

Preprint, 2017.

J. Jomo, N. Zander, M. Elhaddad, A. Özcan, S. Kollmannsberger, R-P. Mundani, E. Rank.

*Parallelization of the multi-level hp-adaptive finite cell method.*

Computers and Mathematics with Applications, 2017.

D. D'Angella, S. Kollmannsberger, E. Rank, A. Reali.

*Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis.*

Computers Methods in Applied Mechanics and Engineering, 2017.

S. Hubrich, P. Di Stolfo, L. Kudela, S. Kollmannsberger, E. Rank, A. Schröder.

*Numerical integration of discontinuous functions: moment fitting and smart octree.*

Computational Mechanics, 2017.

O. Bas, E. De-Juan-Pardo, C. Meinert, D. D’Angella, J. Baldwin, L. Bray, R. Wellard, S. Kollmannsberger, E. Rank, C. Werner, T. Klein, I. Catelas, D. W. Hutmacher.

*Biofabricated soft network composites for cartilage tissue engineering.*

Biofabrication, 2017.

## 2016:

D. D'Angella, N. Zander, S. Kollmannsberger, F. Frischmann, E. Rank, A. Schröder, A. Reali.

*Multi-Level hp-Adaptivity and Explicit Error Estimation.*

Advanced Modeling and Simulation in Engineering Sciences, pp. 1-18, Springer, 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

## 2017:

A. Matei, S. Sitzmann, K. Willner, B. Wohlmuth.

A mixed variational formulation for a class of contact problems in viscoelasticity.

Submitted, 2017.

S. Wulfinghoff , H. R. Bayat , A. Alipour, S. Reese.

*A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations.*

Computer Methods in Applied Mechanics and Engineering, 2017.

S. Reese, H. R. Bayat, S. Wulfinghoff.

*On an equivalence between a discontinuous Galerkin method and reduced integration with hourglass stabilization.*

Computer Methods in Applied Mechanics and Engineering, Preprint, 2017

H. R. Bayat, S. Wulfinghoff, S. Reese.

*On the use of reduced integration in combination with discontinuous Galerkin discretization – application to volumetric and shear locking problems.*

Advanced Modeling and Simulation in Engineering Sciences, Preprint, 2017.

## 2016:

J. Krämer, C. Wieners, B. Wohlmuth, L. Wunderlich.

*A hybrid weakly nonconforming discretization for linear elasticity.*

Proceedings in Applied Mathematics and Mechanics, 2016.

T. Horger, B. Wohlmuth, L. Wunderlich.

*Reduced basis isogeometric mortar approximations for eigenvalue problems*

in vibroacoustics.

Model Reduction for Parametrized, 2016.

T. Horger, A. Reali, B. Wohlmuth, L. Wunderlich.

*Improved approximation of eigenvalues in isogeometric methods for*

*multi-patch geometries and Neumann boundaries.*

Cornell University Library, 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.

## Isogeometric and stochastic collocation methods for nonlinear probabilistic multiscale problems in solid mechanics

## 2017:

F. Fahrendorf, L. De Lorenzis, H. Gomez.

*Reduced integration at superconvergent points in isogeometric analysis.*

Submitted to: Computer Methods in Applied Mechanics and Engineering, 2017

J. Kiendl, E. Marino, L. De Lorenzis.

*Isogeometric collocation for the Reissner-Mindlin shell problem.*

Submitted to: Computer Methods in Applied Mechanics and Engineering, 2017

O. Weeger, B. Narayanan, L. De Lorenzis, J. Kiendl, M. L. Dunn.

*An isogeometric collocation method for frictionless contact of Cosserat rods.*

Computer Methods in Applied Mechanics and Engineering, 2017.

## 2016:

H. Gomez, L. De Lorenzis.

*The variational collocation method. *

Computer Methods in Applied Mechanics and Engineering, 2016.

## 2015:

R. Kruse, N. Nguyen-Thanh, L. De Lorenzis, T.J.R. Hughes.

*Isogeometric collocation for large deformation elasticity and frictional contact problems.*

Computer Methods in Applied Mechanics and Engineering, 2015

## First-order system least squares finite elements for finite elasto-plasticity

## 2017:

A. Schwarz, K. Steeger, M. Igelbüscher, and J. Schröder.

*Different approaches for mixed lsfems in hyperelasticity.*

Computational Mechanics, submitted.

J. Schröder, M. Igelbüscher, A. Schwarz, G. Starke.

*A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity.*

Computer Methods in Applied Mechanics and Engineering, 317:400–418, 2017.

## 2016:

P. Bringmann, C. Carstensen, G. Starke.

*An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates.*

Submitted to: SINUM, 2016.

A. Schwarz, K. Steeger, M. Igelbüscher, and J. Schröder.

*Comparison of different least-squares mixed finite element formulations for hyperelasticity.*

Proceedings in Applied Mathematics and Mechanics, 16:239–240, 2016.

M. Igelbüscher, J. Schröder, A. Schwarz.

*On the performance of the Prange- Hellinger-Reissner finite element formulation for elasto-plasticity at small strains.*

Proceedings in Applied Mathematics and Mechanics, 16:203–204, 2016.

R. Krause, B. Müller, G. Starke.

*An adaptive least-squares mixed finite element method for the Signorini problem. *

Numerical Methods for Partial Differential Equations, 2016.

## Advanced Finite Element Modeling of 3D Crack Propagation by a Phase Field Approach

## 2017:

T. Noll, C. Kuhn, R. Müller.

*A Monolithic Solution Scheme for a Phase Field Model of Ductile Fracture.*

Submitted to: Proceedings in Applied Mathematics and Mechanics, 2017.

## 2016:

T. Noll, C. Kuhn, R. Müller.

*Investigation of a Phase Field Model for Elasto-plastic Fracture.*

Proceedings in Applied Mathematics and Mechanics, 2016.

C. Kuhn, T. Noll, R. Müller.

*On phase field modeling of ductile fracture. *

GAMM- Mitteilungen, 2016.

C. Kuhn, R. Müller.

A discussion of fracture mechanisms in heterogeneous materials by means of configurational forces in a phase field fracture model.

Computer Methods in Applied Mechanics and Engeneering, 2016.

## 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. Bilgen, A. Kopanicakova, R. Krause, K. Weinberg.

*A phase-field approach to conchoidal fracture.*

Under review at Meccanica, 2017.

T. Dally, K. Weinberg, C. Bilgen.

*Cohesive elements or phase-field fracture: Which method is better for reliable analyses in dynamic fracture?*

Submitted to: Engineering Fracture Mechanics, 2017.

C. Bilgen, A. Kopanicakova, R. Krause, K. Weinberg.

*A phase-field approach to pneumatic fracture.*

submitted to: Proceedings in Applied Mathematics and Mechanics, 2017.

K. Weinberg.

*A phase-field approach to material degradation.*

14th Joint European Thermodynamics Conference, 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.

M. Thomas, C. Bilgen, K. Weinberg.

*Analysis and Simulations for a Phase Field Fracture Model at Finite Strains.*

Preprint, 2017.

## 2016:

C. Bilgen, C. Hesch, K. Weinberg.

*A polyconvex strain-energy split for a high-order phase-field approach to fracture.*

Proceedings in Applied Mathematics and Mechanics, 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.

## A novel smooth discretization approach for elasto-plastic contact of bulky and thin structures

## 2017:

A. Seitz, W.A. Wall, A. Popp.

*A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation employing non-smooth nonlinear complementarity functions.*

submitted to: Advanced Modeling and Simulation in Engineering Sciences, 2017.

C. Meier, M.J. Grill, W.A. Wall, A. Popp.

*Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures.*

submitted to: International Journal of Solids and Structures, 2017.

## 2016:

P. Farah, M. Gitterle, W.A. Wall, A. Popp.

*Computational wear and contact modeling for fretting analysis with isogeometric dual mortar methods.*

Key Engineering Materials 681:1-18, 2016

A. Seitz, P. Farah, 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:

A. Seitz, A. Popp, W. Wall.

*A semi-smooth Newton method for orthotropic plasticity and frictional contact at finite strains. *

Computer Methods in Applied Mechanics and Engineering, 2015.