Everybody is warmly welcome.

]]>Speaker: **Alexei Gazca Orozco**

Title: **Nonlinear iterative approximation of steady flow of chemically reacting fluids**

Abstract: In this talk, I will present some recent results obtained in collaboration with P. Heid and E. Süli on an iterative scheme for computing the solutions of a system describing an incompressible fluid with power-law-like rheology, with a power-law exponent depending on a scalar variable that solves an advection-diffusion PDE; in particular, this exponent varies in space. Under small data assumptions, we prove that a Zarantonello-type iteration converges to the (unique) solution of the problem. The proposed iteration scheme is remarkably simple and it amounts to solving a linear Stokes-Laplace system at each step. I will conclude with numerical experiments and some discuss possible uses as a nonlinear preconditioner.

]]>Speaker: **Bangwei She**

Title: **A linear and monolithic FEM for fluid-shell interaction: stability and error estimates**

Abstract: We propose a linear and monolithic scheme for the approximation of a fluid-structure interaction problem, that is a flexible elastic plate interacting with a viscous incompressible fluid. For the time discretization we take the backward Euler method. Concerning the space discretization, we use P1-bubble/P1/P1 elements for the approximation of the fluid velocity, pressure, and the structure displacement. With the application of the arbitrary-Lagrange-Euler (ALE) method we derived a linear scheme on the reference domain, meaning that re-meshing is not needed during the simulation. We prove the unconditional stability of the numerical solution as well as the linear convergence rate with respect to the size of the time step ?t and mesh h. Finally, we present the numerical experiments to validate the theoretical results.

]]>Speaker: **Peter Kottman**

Title: **On Pitfalls of Using Diffuse Interface Methods for Problems Involving Flow across an Interface**

Abstract: Problems with mass flux across non-material interfaces (e.g. phase interfaces) occur in numerous applications of continuum mechanics, such as geophysics, material science, and biology. While from a physical point of view these problems are viewed as systems of governing equations solved on subdomains with jump conditions prescribed at the surface representing the interface, the numerical solutions of the problems usually treat the interface as a layer of finite thickness, where quantities change rapidly but smoothly, and solve the governing equations in the entire domain. This diffuse interface approach is effective and widely used. On the basis of heuristic results from the field of geodynamics, we demonstrate that these two points of view are inconsistent, provide a framework for a rigorous study of sharp limits the diffuse interface solutions in the form of the Colombeau algebra, and discuss the issues arising in efforts to generalize this idea for more complicated models.

]]>Speaker: Michal Bathory

Title: Existence of a weak solution for thermoviscoelastic incompressible fluids

Abstract: Properties of viscoelastic fluids usually depend on temperature in a substantial way. However, including a temperature evolution into conventional viscoelastic models leads to a badly-behaved system of nonlinear PDEs, where the integrability of the velocity gradient can no longer be read from the Navier-Stokes equation. By relying on the temperature and entropy inequalities instead, we show existence of a weak solution under optimal growth assumptions on the material coefficients.

]]>Speaker:** Alexei Gazca Orozco**

Title: **Heat-conducting Incompressible Fluids and Weak-Strong Uniqueness**

Abstract: In this talk, I will present some recent results obtained in collaboration with V. Patel (Oxford) in connection with a system describing an incompressible heat-conducting incompressible fluid. I will introduce the notion of a dissipative weak solution of the system and highlight the connections and differences to the existing approaches in the literature. One of the advantages of the proposed approach is that the solution satisfies a weak-strong uniqueness principle, which guarantees that the weak solution will coincide with the strong solution, as long as the latter exists; moreover, the solutions are constructed via a finite element approximation, leading (almost, not quite) to the first convergence result for the full system including viscous dissipation.

]]>Speaker: **Stanislaw Stupkiewicz**

Title: **Automatic differentiation in computational plasticity**

Abstract: In the talk, I will present a general (and personal) look at computational plasticity and nonlinear solid mechanics. Classical incremental equations of rate-independent elastoplasticity will be briefly discussed along with their computational treatment involving the return-mapping algorithm, iterative-subiterative Newton scheme, and consistent linearization. While all these notions are well known, less known is the related approach relying on automatic differentiation (AD). This approach allows us to automatize several tedious steps in computer implementation of complex constitutive models. I will thus briefly present the basic idea of automatic differentiation and show how it can be used in computational plasticity. The approach will be illustrated by some examples of our recent research, including modelling of pseudoelasticity in shape memory alloys and crystal plasticity.

]]>Speaker: **Karel Tůma**

Title: **Contactless rebound of elastic bodies in a viscous incompressible fluid**

Abstract: We investigate the phenomenon of particle rebound in a viscous incompressible fluid environment We focus on the important case of no-slip boundary conditions, for which it is by now classical that, under certain assumptions, collisions cannot occur in finite time. In a simplified framework, we provide conditions which allow to prove that rebound is possible even in the absence of a topological contact. Our results lead to conjecture that a qualitative change in the shape of the solid is necessary for obtaining a physically meaningful rebound in fluids. We support the conjecture by comparing numerical simulations performed for the reduced model with finite element solutions obtained for corresponding well-established PDE systems describing elastic solids interacting with incompressible fluids. This is a joint work with Giovanni Gravina, Sebastian Schwarzacher and Ondřej Souček.

]]>Speaker: **Malte Kampschulte**

Title: **Viscoelastodynamics from a mathematical point of view**

Abstract: The aim of this talk is to give an overview of the current state of the mathematical study of the (visco-)elastodynamics of (bulk) solids, with a focus on existence theory. In the spirit of the interdisciplinary nature of the seminar, the goal will be to give an insight into what can and what cannot be done (yet), with the hope that this will prove useful to those whose work intersects the theory from the side of modelling, numerics, coupling with other theories and so on. In particular I will detail the ambivalent nature of the involved nonlinearities, which are the unavoidable source of some of the biggest problems and at the same time contain the keys to their solution. For this I will try to present the intuition behind some older and some more recent results on the topic and contrast the different approaches.

]]>Speaker: **Ondřej Pejcha**

Title: **Death of single and binary stars**

Abstract: I will provide an overview of my results in the theory of core-collapse supernova explosions and catastrophic interactions of binary stars. Many of these results were obtained by solving various modifications of Euler equations of compressible hydrodynamics. I will specifically mention steady-state solutions obtained by relaxation, smoothed particle hydrodynamics combined with flux-limited radiative diffusion, and 2D and 3D finite volume hydrodynamics with adaptive mesh refinement, on moving meshes, or combined with radiation transport. I will conclude by discussing ideas about future work with discontinuous Galerkin on curvilinear meshes.

]]>