NEČAS SEMINAR ON CONTINUUM MECHANICS
organized by the Mathematical Institute of the Charles University
each Monday at 15:40
in the MFF UK building,
Sokolovská 83, lecture room K1, 2^{nd}
floor,
proceeds with the following presentations:

Dr. Jaroslav Hron (University of Dortmund):  A monolithic multigrid FEM solver for fluid structure interaction and numerical benchmarking  Abstract: A monolithic, fully coupled approach using the ALE formulation is used to discretize and solve the problem of time dependent interaction between an incompressible viscous fluid and an incompressible elastic solid. For the discretization the FEM method is used while the solver is based on approximate Newton method combined with multigrid solver for the solution of the linear systems. To investigate accuracy, performance and efficiency of the solver a simple problem configuration is introduced as a benchmark. 



Prof. Dr. Michael Hinze (Technical University Dresden):  PDE constrained optimization I  Abstract: This is a first lecture of the course that continues on Tuesday Jan 10, 15:40 in K4 by its second part, and finishes on Thursday Jan 12, 14:00 in K3. 



Michal Beneš, Eduard Feireisl, Josef Málek  NCMM: Centrum Jindřicha Nečase pro matematické modelování  Abstract: Cílem tohoto nestandartního semináře (valné hromady) je přiblížit poslání a cíle "Nečasova Centra pro matematické modelování", shrnout obsahovou i finanční stránku projektu, strukturu centra a především otevřít prostor pro vědeckou činnost centra. 



Prof. Piotr Mucha (University of Warsaw):  Stefan problem with GibbsThomson correction  Abstract: I would like to investigate the quasistationary Stefan problem with GibbsThomson correction. The main subject will be the proof of existence of unique solutions for arbitrary initial surface. The system is equivalent to the parabolic equation of the third order, hence a suitable approach is required to obtain the optimal result from the regularity point of view. The considerations will be done in the L_pspaces. 



Dr. Petr Knobloch, Ph.D. (KNM MFF UK):  Numerické řešení rovnic konvekcedifúze metodou konečných prvků  Abstract: If convection strongly dominates diffusion, the solutions of convectiondiffusion equations typically contain interior and boundary layers and solutions of Galerkin finite element discretizations exhibit in general unwanted spurious oscillations. To enhance the stability and accuracy of these discretizations, various stabilization strategies have been developed during the past three decades. One of the most efficient procedures is the streamline upwind/PetrovGalerkin (SUPG) method developed by Brooks and Hughes. Unfortunately, the SUPG method does not preclude spurious oscillations localized in narrow regions along sharp layers. Although these oscillations are usually small in magnitude, they are not permissible in many applications. Therefore, various terms introducing artificial crosswind diffusion in the neighborhood of layers have been proposed to be added to the SUPG formulation in order to obtain a method which is monotone or which at least reduces the local oscillations. This procedure is referred to as discontinuity capturing (or shock capturing). The literature on discontinuitycapturing methods is rather extended and the various numerical tests published in the literature do not allow to draw a clear conclusion concerning their advantages and drawbacks Therefore, our aim is to provide a review of discontinuitycapturing methods and to compare these methods computationally by means of several test problems. 



Prof. Dr. Wolfgang Wendland (University of Stuttgart):  Boundary Element Methods: Boundary Integral Equations and Variational Problems  Abstract: This is the first lecture of the short course that continues on Tuesday March 21, 15:45 (at K2) by the second part "Finite Elements on the Boundary" and finishes on Thursday, March 23, 14:00 (at K3) by the lecture "Efficient Solution Algorithms and Some Industrial Applications". 



Prof. RNDr. Jan Malý, DrSc. (KMA MFF UK):  Problémy s řetízkovým pravidlem v teorii ODR a PDR  Abstract: Otázka za jakých předpokladů platí v nějakém smyslu vzorce o derivování složené funkce, vyvstává v teorii soustav obyčejných diferenciálních rovnic, v DiPernaLionsově teorii toků (flows), teorii HamiltonJacobiho rovnic i v zákonech zachování. Konkrétně, derivujeme výraz $(h\circ u) B$, kde $h\in C^1$, $u\in L^{\infty}$ a $B\in BV$. 



Prof. Dr. Barbara Wohlmuth (University of Stuttgart):  Mortar discretizations and their applications  Abstract: This is the first lecture of the short course that continues on Tuesday April 4, 15:45 at K2 by the second part and finishes on Thursday, April 6, 14:00 at K3. 



doc. ing. Tomáš Roubíček, DrSc. (MFF UK):  Ionizované nestlačitelné směsi  Abstract: Formulace modelu nestlačitelných chemicky reagujících ionizovaných směsí a důkaz existence řešení jak pro newtonovský případ tak pro speciální nenewtonovské případy. 




Seminář se nekoná  Velikonoce  



Prof. RNDr. Jan Malý, DrSc. (KMA MFF UK):  Problémy s řetízkovým pravidlem v teorii ODR a PDR  část II  Abstract: Otázka za jakých předpokladů platí v nějakém smyslu vzorce o derivování složené funkce, vyvstává v teorii soustav obyčejných diferenciálních rovnic, v DiPernaLionsově teorii toků (flows), teorii HamiltonJacobiho rovnic i v zákonech zachování. Konkrétně, derivujeme výraz $(h\circ u) B$, kde $h\in C^1$, $u\in L^{\infty}$ a $B\in BV$. 




Seminář se nekoná  státní svátek  




Seminář se nekoná  státní svátek  



RNDr. Antonin Slavik, Ph.D. (KDM MFF UK):  An introduction to product integration  Abstract: Product integral might be considered as a multiplicative analogy of the classical additive integral. The notion is useful especially in the field of ordinary differential equations, but has also applications in mathematical physics, probability and statistics. The presentation will take less than half an hour. 



Dr. Soeren Bartels (Humboldt Universitaet zu Berlin, Germany):  Approximation of Harmonic Maps  Gradient Flow Approaches vs. Iterative Minimization  Abstract: Harmonic maps are stationary points of the Dirichlet energy among vector fields with values in the unit sphere. Owing to the nonconvex constraint, harmonic maps are nonunique and fail to admit higher regularity properties. Moreover, the constraint prohibits the use of standard tools for their numerical approximation. In this talk we discuss stability and weak convergence of three numerical approaches to the reliable approximation of harmonic maps. 



Professor Giovanni Pallotti, Dr., Ing. (Mech. Eng.), Dr.(Phys.) (University of Bologna):  Mechanical Properties of Great Arterial Wall and Clinical Implication  



15:40  Prof. Luisa Consiglieri (Department of Mathematics FCUL, Lisboa, Portugal):  A (pq) coupled system in elliptic nonlinear problems with nonstandard boundary conditions
 

17:20  
Introduction of the guests and members of the Nečas Center for Mathematical Modeling
 




INAUGURAL SEMINAR OF the Nečas Center
 



15:40  Prof. Dr. Dietmar Kröner (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany):  Well balanced schemes for conservation laws  Abstract: There are many numerical schemes for hyperbolic conservation laws, which have some problems, if there is a source term and if a stationary solution has to be computed. There are many ideas to overcome this problem. One of them goes back to Greenberg et al. and needs a special structure of the source term. We will present this idea and extend it to problems in multi space dimensions and to systems with nonconservative source terms in 1D. Furthermore we will give a convergence proof for this method, if applied to the initial boundary value problem for scalar conservation laws in 1D. In that case the definition of entropy process solutions for initial boundary value problems will be used. 



15:40  Prof. Dr. Herbert Amann (Mathematical Institute University of Curych, Curych, Switzerland):  Parabolic equations on singular manifolds  Abstract: We report on a new, rather simple and flexible approach to the study of linear and nonlinear parabolic equations on manifolds with corners, cusps, edges etc. The basic technique is illustrated for reactiondiffusion equations on a manifold with a cusp or a cuspoindal wedge. 

17:20  Prof. Dorin Bucur (Département de Mathématiques Université de Metz, Metz, France):  Γconvergence and domain dependence of solutions of PDE's (part 1 of 4)  



15:40  Prof. Dorin Bucur (Département de Mathématiques Université de Metz, Metz, France):  Γconvergence and domain dependence of solutions of PDE's (part 3 of 4)  

17:20  Prof. Frank Ettwein (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany):  Micropolar electrorheological fluids: existence of weak solutions in a degenerate stationary case
 



15:40  Prof. Ziemmer (Dep. of Mathematical Sciences, University of Bath, UK):  On waves in discrete models of elasticity and plasticity
 

17:20  Prof. Pavol Quittner (Dep. of Applied Mathematics and Statistics Comenius University, Bratislava, Slovakia):  Qualitative theory of semilinear parabolic equations and systems (part 9 of 12)
 



15:40  Prof. Konstantina Trivisa (Dep. of Mathematics University of Maryland, College Park MD, USA):  Hyperbolic Systems of Conservation Laws: Wellposedness and Qualitative Behavior of the Solutions
 

17:20  Prof. Pavol Quittner (Dep. of Applied Mathematics and Statistics Comenius University, Bratislava, Slovakia):  Qualitative theory of semilinear parabolic equations and systems (part 11 of 12)
 



15:40  Prof. Dr. Werner Varnhorn (Fachbereich für Mathematik und Informatik Universität Kassel, Kassel, Germany):  The Navier Stokes equations with Lagrangian differences 1  Abstract: The steady motion of a viscous incompressible fluid in a bounded domain can be described by the nonlinear Navier Stokes equations (N). We describe an approximation method for (N) by using Lagrangian differences. The method leads to a sequence of unique approximate solutions containing a convergent subsequence with limit function v solving (N) weakly.


17:20  Prof. Dr. Werner Varnhorn (Fachbereich für Mathematik und Informatik Universität Kassel, Kassel, Germany):  The Navier Stokes equations with Lagrangian differences 2  Abstract: Replacing the nonlinear convective term in the Navier Stokes equations (N) by central Lagrangian differences we obtain an energy conserving approximation. The resulting regularity properties of the limit function v (compare Part 1) are sufficient for the limit procedure in the nonlinear term. Some details of the proofs are carried out.




15:40  Ing. R. Liska (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha):  Arbitrary Lagrangian Eulerian (ALE) Method for Laser Plasma Simulations
 

16:10  Ing. T. Oberhuber (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha):  Numerical scheme for the Willmore flow
 

17:00  Ing. R. Straka (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha):  Model of coal combustion in a furnace
 

17:30  Ing. V. Minárik (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha):  Mathematical Model of Dislocation Dynamics
 



15:45  Prof. Dr. Robert Finn (Stanford University):  The capillarity problem for compressible fluids  Abstract: Current literature on fluid configurations under capillary attractions generally is based on postulates introduced in 1830 by Gauss. By neglecting bulk energy variations within the fluid, these postulates lead to an essentially geometrical problem. I will present an example indicating that bulk energy terms can indeed be significant, and I will derive and examine the equations obtained by taking account of energy changes imposed by fluid compressibility. The formal character of the mathematical problem then changes, but remains geometrical. Solutions of the new equations share some striking features that occur with the classical equations, but also new exotic behavior appears that was previously not encountered. Experimental tests of the predictions may be feasible.


17:15  Prof. Dr. Friedemann Schuricht (Universität zu Köln):  A new mathematical foundation for contact interactions in continuum physics  Abstract: The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. The talk presents a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a more precise description of contact phenomena than before.




15:45  Dr. Lars Diening (University of Freiburg, Germany):  Convergence of Adaptive Finite Element Methods for the pLaplace  Abstract: We study adaptive finite element methods for the $p$Laplacian Equation using piecewise linear, continuous functions. The error is measured by means of the quasinorm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. Moreover, we show that the algorithm produces (almost) optimal meshes with respect to the degress of freedom. This extends the results of Stevenson to the nonlinear case. All results are obtained without extra marking for the oscillation.


17:15  Dr. Giuseppe Tomassetti (University of Rome, Italy):  Derivation of the ReissnerMindlin plate theory from Gamma convergence
 



16:00  Prof. RNDr. Jaroslav Kurzweil, DrSc. (MU AV ČR):  Matematikovy vzpomínky na čtyřicátá až šedesátá léta  Abstract: Přednáška bude doplněna o vystoupení kvarteta violončelistů a zpěv písní vánočních 


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