Numerical methods for stochastic conservation laws
A class of nonlinear evolution equations of second order
Multi-index Monte Carlo and Multi-index Stochastic Collocation
Hyperbolic-Elliptic models for two-phase flow in porous media
Rough paths and rough partial differential equations
The universe in a computer: how mathematical and numerical methods are essential
Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients
Comments on the Galilean limits of Maxwell's equations
Convex relaxation, graph cut and continuous max-flow algorithms for image processing and computer vision.
Parameter-robust finite element discretization and its preconditioning for Biot's consolidation model in poroelasticity
Jan Martin Nordbotten (University of Bergen) will give a talk about
Finite volume methods for elasticity and poro-elasticity
Abstract: We introduce a new class of cell-centered finite volume methods for elasticity and poro-elasticity. This class of discretization methods has the advantage that the mechanical discretization is fully compatible (in terms of grid and variables) to the standard cell-centered finite volume discretizations that are prevailing for commercial simulation of multi-phase flows in porous media.
For a specific variant of the proposed discretization, we give an overview of a convergence proof in the setting of isotropic elasticity, and address from a theoretical perspective the issues of a discrete Korn's inequality and robustness with respect to locking. Furthermore, we give numerical results for both structured and unstructured grids for both elasticity and poro-elasticity. The talk concludes with an application to simulation of fractured and fracturing porous media.
Dongho Chae (Chung-Ang University, Korea) will give a seminar talk entitled
On the self-similar blow-up for the compressible Euler equations
Abstract: The problem of ﬁnite time blow-up/global regularity of the 3D incompressible Euler equations is an outstanding problem in mathematical ﬂuid mechanics. On the other hand, the scenario of self-similar type blow-up is a natural candidate of blow-ups in various nonlinear partial differential equations such as the porous medium equation and the nonlinear Schrödinger equations. We also mention that for the closely related incompressible Navier-Stokes equations the question of self-similar blow-up was raised by J. Leray in 1930, and was negatively answered by J. Necas, M. Ruzicka and V. Sverak in 1996. In this talk we present the progress of study during the last several years on the self-similar blow-up for the Euler equations.
Johanna Ridder (University of Oslo) will give a talk about
Analysis of a finite difference method for two-dimensional incompressible magnetohydrodynamics
Abstract: We consider the magnetohydrodynamics equations for a viscous incompressible resistive fluid in two dimensions. For these equations we analyse a semi-discrete finite difference scheme that is based on a staggered grid and is energy preserving. We show an a priori H^1-bound and the convergence of the scheme.
Jeonghun J. Lee (Aalto University, Helsinki) will give a talk about
On unified analysis of mixed methods for elasticity with weakly symmetric stress.
Abstract: We introduce a framework to construct and analyze mixed finite elements for elasticity with weakly symmetric stress. The framework is based on a connection between mixed methods for elasticity and mixed methods for Stokes equations. We show that some new finite elements can be obtained from it with optimal error bounds.
Rajib Dutta (University of Oslo) will give a seminar talk on
Operator splitting methods for Benjamin-Ono (BO) equation
Abstract: We consider the BO equation which describes one-dimensional internal waves in deep water. In this talk, we show that both Godunov and Strang splitting methods converge with the expected rates if the initial data are sufficiently smooth. We also present a proof of convergence of a fully discrete finite difference scheme for this equation.
Giuseppe Coclite, University of Bari.
In this lecture we consider a model for the harvesting of marine resources, described by a parabolic equation. Since the cost functionals have sublinear growth with respect to the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies. The results were obtained in collaboration with Professor Mauro Garavello.
A General Framework for Implementing Conservation-law Solvers
Dr. Ujjwal Koley from University of Würzburg, is going to talk about Operator splitting methods for Korteweg de-Vries (KdV) equation
Ilia Musco will give a seminar.
Martin Licht (University of Bonn) will give a talk about
On equilibrated a posteriori error estimation for Nedelec-elements
Arbitrarily high order numerical schemes that converge to entropy measure valued solutions of systems of hyperbolic conservation laws.
Analysis and Application of Polygonal and Serendipity Finite Element Methods
This lecture series will be based on the introduction, chapters 1 and 2 of the book "Topics in Optimal Transportation" by Cedric Villani.