Publications & Preprints of Dorothee Knees
Publications
- F. Rörentrop, S. Boddin, D. Knees, J. Mosler,
A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics,
accepted in Computer Methods in Applied Mechanics and Engineering, 2024,
arXiv:2403.07461, 2024. (pdf)
- D. Knees, P. Neff, S. Owczarek, A global higher regularity result for the static relaxed micromorphic model on smooth domains, accepted in Proc. R. Soc. Edinb., Sect. A, Math. 2024. (arXiv, DOI: https://doi.org/10.1017/prm.2024.63)
- D. Knees, S. Thomas,
Optimal control of a rate-independent system constrained to parametrized balanced viscosity solutions,
SIAM Journal on Control and OptimizationVolume 61, Issue 2, pp. 361-923, 2023.
(arXiv,
SIAM)
- D. Knees, S. Owczarek, P. Neff,
A local regularity result for the relaxed micromorphic model based on inner variations,
J. Math. Anal. Appl. 519, Issue 2, 15 March 2023, 126806, arXiv:2208.04821, 2022. (pdf)
- D. Knees, C. Meyer, M. Sievers,
Optimal control of non-convex rate-independent systems via vanishing viscosity – The finite dimensional case.
Pure Appl. Funct. Anal. 7, No. 5, 1733-1766 (2022).
(link)
-
D. Knees, A, Schröder, V. Shcherbakov,
Fully discrete
approximation schemes for rate-independent crack evolution,
Philosophical Transactions A, issue on “Non-smooth variational problems and applications”, published
online on 26th September 2022.
-
R, Herzog, D. Knees, C. Meyer, M. Sievers,
A. Stötzner, S. Thomas
Rate-Independent Systems and Their Viscous Regularizations:
Analysis, Simulation, and Optimal Control,
in: M. Hintermüller, R. Herzog, C. Kanzow, M. Ulbrich, S. Ulbrich (eds.),
Non-smooth and complementarity-based distributed parameter systems. Simulation and hierarchical optimization.
ISNM. International Series of Numerical Mathematics 172. Cham: Birkhäuser, 2022. (link)
-
D. Knees, V.
Shcherbakov,
A penalized version of the local minimization scheme for rate-independent systems,
Appl. Math. Lett. 115, Article ID 106954, 2021. (link)
- D. Knees, C. Zanini,
Existence of parameterized BV-solutions for rate-independent systems with
discontinuous loads,
Discrete Contin. Dyn. Syst., Ser. S
14, No. 1, 121-149, 2021.
(pdf)
- D. Knees,
Convergence analysis of time-discretisation schemes for
rate-independent systems,
ESAIM, Control Optim. Calc. Var., vol. 25, article 65, 2019.
DOI: https://doi.org/10.1051/cocv/2018048.
(pdf)
- D. Knees, R. Rossi, C. Zanini
Balanced Viscosity solutions to a rate-independent system for damage,
Eur. J. Appl. Math.,
vol. 30, pp. 117-175, 2019;
(published online Jan 2018).
(pdf)
- D. Knees, M. Negri,
Convergence of alternate minimization schemes for phase field fracture and damage,
Mathematical Models and Methods in Applied Sciences (M3AS),
vol. 27(9), pp. 1743-1794, 2017.
(pdf)
- H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci (eds.),
PDE 2015: Theory and Applications of Partial Differential Equations,
proceedings of PDE 2015, DCDS-S Discrete Contin. Dyn. Syst. Ser. S, vol.
10(4), 2017.
- H. Hanke, D.Knees,
A phase-field damage model based on evolving microstructure,
Asymptotic Analysis, vol. 101(3), pp. 149-180, 2017.
(pdf)
- R. Haller-Dintelmann, A. Jonsson, D. Knees, J. Rehberg,
Elliptic and parabolic regularity for
second order divergence operators with mixed boundary conditions.
Mathematical Methods in the Applied Sciences, vol. 39(17), pp. 5007-5026, 2016.
(pdf, accepted version)
- D. Knees, R. Rossi, Ch. Zanini,
A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains,
Nonlinear Analysis Series B: Real World Applications, vol. 24, pp. 126-162 , 2015.
(pdf, article)
- H. Hanke, D. Knees,
Homogenization of elliptic systems with non-periodic, state dependent coefficients,
Asymptotic Analysis, vol. 92,pp. 203-234, 2015.
(pdf)
- D. Knees, R. Kornhuber, Chr. Kraus, A. Mielke, J. Sprekels.
C3 -- Phase transformation and separation in solids.
"MATHEON -- Mathematics for Key Technologies" in EMS Series in Industrial and Applied Mathematics, vol. 1(1): 189-203, 2014.
- D. Knees, R. Rossi, C. Zanini,
A vanishing viscosity approach to a rate-independent damage model,
Mathematical Models and Methods in Applied Sciences, vol.23(04), pp. 565-616, 2013.
(preprint)
- A. Fiaschi, D. Knees, S. Reichelt,
Global higher integrability of minimizers of variational
problems with mixed boundary conditions,
Journal of Mathematical Analysis and Applications, vol. 401, pp. 269-288, 2013.
(pdf)
- D. Knees, A. Schröder,
Global spatial regularity for elasticity models with cracks,
contact and other nonsmooth constraints,
Mathematical Methods in the Applied Sciences.
Special Issue: Perspectives in Continuum Mechanics,
vol. 35(15), pp. 1859-1884, 2012.
(pdf)
- D. Knees, A. Schröder,
Computational aspects of quasi-static crack propagation,
Discrete and Continuous Dynamical Systems - Series S (DCDS-S),
vol. 6(1), pp. 63-99, 2013.
(pdf)
- A. Fiaschi, D. Knees, U. Stefanelli,
Young measure quasi-static damage evolution,
Arch. Rational Mech. Anal., vol. 203(2), pp. 415-453, 2012.
- D. Knees,
Global spatial regularity for a regularized elasto-plastic model,
GAMM-Mitteilungen, vol. 34(1), pp. 21-27,2011.
- D. Knees,
On global spatial regularity and convergence rates for time dependent elasto-plasticity,
Mathematical Models and Methods in Applied Sciences (M3AS). vol. 20(10), pp. 1823-1858, 2010.
(Preprint)
- P. Gruber, D. Knees, S. Nesenenko, M. Thomas,
Analytical and numerical aspects of time-dependent problems with internal variables,
ZAMM, Z. Angew. Math. Mech., vol. 90(10-11), pp. 861-902, 2010.
(pdf)
- D. Knees, C. Zanini, A. Mielke,
Crack growth in polyconvex materials,
Physica D, vol. 239(15), pp. 1470 - 1484 2010.
(Preprint)
- D. Knees,
On global spatial regularity in elasto-plasticity
with linear hardening,
Calculus of Variations and Partial Differential Equations, vol.36(4), pp. 611-625, 2009.
(Preprint)
- D. Knees, A. Mielke, C. Zanini,
On the inviscid limit of a model for crack propagation,
Mathematical Models and Methods in Applied Sciences,
vol. 18(9), pp. 1529 - 1569, 2008.
(Preprint)
- D. Knees, P. Neff,
Regularity up to the boundary for nonlinear elliptic
systems arising in time-incremental infinitesimal
elasto-plasticity,
SIAM Journal on Math. Analysis, vol. 40(1),
pp. 21-43, 2008.
(Preprint)
- D. Knees, A. Mielke,
On the energy release rate in finite-strain elasticity,
Mechanics of Advanced Materials and Structures, vol. 15(6),
pp. 421-427, 2008.
- D. Knees, A. Mielke,
Energy release rate for cracks in finite-strain elasticity,
Mathematical Methods in the Applied Sciences, vol. 31(5),
pp. 501-528, 2008.
(Preprint)
- D. Knees,
Global stress regularity for convex and some nonconvex
variational problems on Lipschitz domains,
Annali di Matematica Pura ed Applicata, vol.187,
pp.157-184, 2008.
(Preprint)
- D. Knees,
Griffith-formula and J-integral for a crack in a power-law
hardening material,
Mathematical Models and Methods in Applied Sciences (M3AS),
vol. 16, no.11, p. 1723-1749, 2006.
(Preprint)
- D. Knees, A.-M. Sändig,
Regularity of Elastic Fields in Composites,
in: Multifield Problems in Solid and Fluid Mechanics
(R. Helmig, A. Mielke and B. Wohlmuth, eds.).
Lecture Notes in Applied and Computational Mechanics , Vol. 28,
Springer-Verlag, p. 321-350, 2006. (pdf)
- D. Knees,
Global regularity of the elastic fields of a power-law model on
Lipschitz domains,
Mathematical Methods in the Applied Sciences, vol. 29,
p. 1363-1391, 2006.
DOI: 10.1002/mma.727. (Preprint)
-
D. Knees, A.-M. Sändig,
Stress behaviour in a power-law hardening material,
in: Function Spaces, Differential Operators, and Nonlinear
Analysis (P. Drábek and J. Rákosník eds.),
Proceedings of the Conference held in Milvoy, Bohemiam-Moravian
Uplands, May 28-June 2, 2004;
Mathematical Institute of the Academy of Sciences of the Czech
Republic, Praha, p. 134-151, 2005.
-
D. Knees,
On the regularity of weak solutions of nonlinear transmission
problems on polyhedral domains,
Zeitschrift für Analysis und ihre Anwendungen,
vol. 23, no. 3, pp. 509-546, 2004. (Preprint)
- D. Knees,
Regularity results for transmission problems of linear elasticity
on polyhedral domains,
in: Analysis and simulation of
multifield problems (M. Efendiev, W.L. Wendland, eds.), Springer
Verlag, 2003.
Editor of
- Issue on PDE 2015: Theory and applications of partial differential equations,
Discrete Contin. Dyn. Syst. Ser. S, 10, No.4 (2017), edited by
H.-C. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci.
-
Nonsmooth Models in Continuum Mechanics - Analysis and Optimization,
GAMM-Mitteilungen, 40, No. 3-4 (2018), edited by C. Meyer, D. Knees, R. Herzog.
Preprints
- D. Knees, P. Neff, S. Owczarek, Global regularity for a physically nonlinear version of the relaxed micromorphic model on Lipschitz domains, arXiv:2403.17451, 2024. (pdf)
- S. Boddin, F. Rörentrop, D. Knees, J. Mosler,
Approximation of balanced viscosity solutions of a rate-independent damage model
by combining alternate minimization with a local minimization algorithm,
arXiv:2211.12940, 2022. (pdf)
-
D. Knees, A.-M. Sändig (Hrsg.),
Nichtlineare Funktionalanalysis mit Anwendungen in der
Festkörpermechanik,
Universität Stuttgart, IANS,
Seminarbericht
2004/011
, 2004.
- D. Knees,
On the regularity of weak solutions of a shear thinning fluid of
power-law type,
SFB 404,
Bericht 2003/23.
- D. Knees,
Regularity results for transmission problems for the Laplace and
Lamé
operators on polygonal or polyhedral domains,
SFB 404,
Bericht 2002/10.
PhD thesis
Regularity results for quasilinear elliptic systems of power-law growth in
nonsmooth domains
–Boundary, transmission and crack problems–,
University of
Stuttgart, 2005.
(
pdf)
Diploma thesis
Regularitätsaussagen für
zweidimensionale elastische Felder in Kompositen,
University of Stuttgart, 2001.
(
ps)
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Last modified: 2024-03-15 by Dorothee Knees