15 citations · 28 across the 9 of their papers we have counts for
11 papers
Global regularity for a physically nonlinear version of the relaxed micromorphic model on Lipschitz domains
Dorothee Knees, Sebastian Owczarek, Patrizio Neff
In this paper, we investigate the global higher regularity properties of weak solutions for a linear elliptic system coupled with a nonlinear Maxwell-type system defined on Lipschi…
A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics
Felix Rörentrop, Samira Boddin, Dorothee Knees +1
The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometr…
A global higher regularity result for the static relaxed micromorphic model on smooth domains
Dorothee Knees, Sebastian Owczarek, Patrizio Neff
We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic syst…
Approximation of balanced viscosity solutions of a rate-independent damage model by combining alternate minimization with a local minimization algorithm
Samira Boddin, Felix Rörentrop, Dorothee Knees +1
The modeling of cracks has been an intensely researched topic for decades - both from the mechanical as well as from the mathematics point of view. As far as the modeling of sharp…
A local regularity result for the relaxed micromorphic model based on inner variations
Dorothee Knees, Sebastian Owczarek, Patrizio Neff
In this paper we study local higher regularity properties of a linear elliptic system that is coupled with a system of Maxwell-type. The regularity result is proved by means of a m…
Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads
Dorothee Knees, Chiara Zanini
We study a rate-independent system with non-convex energy and in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-i…
Optimal control of a rate-independent system constrained to parametrized balanced viscosity solutions
Dorothee Knees, Stephanie Thomas
We analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex…
Convergence analysis of time-discretisation schemes for rate-independent systems
Dorothee Knees
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In th…
Balanced Viscosity solutions to a rate-independent system for damage
Dorothee Knees, Riccarda Rossi, Chiara Zanini
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15]…
A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains
Dorothee Knees, Riccarda Rossi, Chiara Zanini
This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is…
Elliptic and parabolic reguarity for second order divergence operators with mixed boundary conditions
Robert Haller-Dintelmann, Alf Jonsson, Dorothee Knees +1
We study second order equations and systems on non-Lipschitz domains including mixed boundary conditions. The key result is interpolation for suitable function spaces. From this, e…