PDE seminar

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Time and place: Sep. 26, 2016 9:15 AM - 10:00 AM, Niels Henrik Abels hus, Undervisningsrom 1036

Numerical methods for stochastic conservation laws

Time and place: Sep. 2, 2016 10:15 AM - 11:00 AM, Undervisningsrom 801, Niels Henrik Abels hus

A class of nonlinear evolution equations of second order

Time and place: June 24, 2016 10:15 AM - 11:00 AM, NHA, room 1036

Multi-index Monte Carlo and Multi-index Stochastic Collocation

Time and place: Jan. 22, 2016 10:15 AM - 11:00 AM, NHA Room 1036

Hyperbolic-Elliptic models for two-phase flow in porous media

Time and place: Nov. 16, 2015 1:15 PM - 3:00 PM, Undervisningsrom 108, NHA hus

Rough paths and rough partial differential equations

Time and place: Oct. 30, 2015 9:15 AM - 10:00 AM, Room 1036 in Niels Henrik Abels hus

The universe in a computer: how mathematical and numerical methods are essential

Time and place: May 28, 2015 10:15 AM - 11:00 AM, room 1036 in Niels Henrik Abels hus

Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

Time and place: Apr. 30, 2015 11:15 AM - 12:00 PM, Room 1036 (Niels Henrik Abels hus)

Comments on the Galilean limits of Maxwell's equations

Time and place: Apr. 27, 2015 11:15 AM - 12:00 PM, Room 1036 (Niels Henrik Abels hus).

Convex relaxation, graph cut and continuous max-flow algorithms for image processing and computer vision.

Time and place: Apr. 10, 2015 10:15 AM - 11:15 AM, NHA B1036

Parameter-robust finite element discretization and its preconditioning for Biot's consolidation model in poroelasticity

Time and place: Mar. 4, 2014 10:15 AM - 11:00 AM, NHA B1036

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.  

Time and place: Feb. 25, 2014 10:15 AM - 11:00 AM, NHA B1036

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.

Time and place: Feb. 21, 2014 2:15 PM - 3:00 PM, NHA B1036

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.

Time and place: Feb. 4, 2014 10:15 AM - 11:00 AM, NHA B81

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.

Time and place: Jan. 31, 2014 2:15 PM - 3:00 PM, NHA B1036

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.  

Time and place: Jan. 14, 2014 10:15 AM - 11:00 AM, B63

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.  

Time and place: Dec. 12, 2013 10:15 AM - 11:00 AM, B1036, NHA

A General Framework for Implementing Conservation-law Solvers

Time and place: Oct. 4, 2013 2:15 PM - 3:00 PM, NHA B1036

Dr. Ujjwal Koley from University of Würzburg, is going to talk about Operator splitting methods for Korteweg de-Vries (KdV) equation

Time and place: Sep. 30, 2013 11:15 AM - 12:00 PM, NHA B1036

Ilia Musco will give a seminar.

Time and place: Aug. 28, 2013 1:15 PM - 2:00 PM, NHA B1036

Martin Licht (University of Bonn) will give a talk about

On equilibrated a posteriori error estimation for Nedelec-elements

Time and place: May 21, 2013 10:15 AM - 11:00 AM, b1025, NHA

Arbitrarily high order numerical schemes that converge to entropy measure valued solutions of systems of hyperbolic conservation laws.

Time and place: May 16, 2013 2:15 PM - 3:00 PM, b1025, NHA

Analysis and Application of Polygonal and Serendipity Finite Element Methods

Time: Mar. 14, 2013
Time: Jan. 17, 2012 10:15 AM - 11:00 AM
In nature, groups of individuals organize globally using only local information. For instance, in a school of fish, there are no external forces to coordinate the group, no leader to guide them. Several mathematical models have been proposed to describe self-organization. In this talk, we will consider two of the most famous models; the Keller-Segel model for bacterial chemotaxis and the Cucker-Smale model for flocking. The emphasis will be on recent mathematical results and remaining open questions. Starting from the microscopic description on particle level, we will discuss the derivation of mesoscopic and macroscopic models at the continuum level. Since the motivation for deriving continuum models is largely numerical, we will also discuss distinct numerical challenges with the resulting models.
Time: Nov. 25, 2011 10:15 AM - 11:00 AM

This lecture series will be based on the introduction, chapters 1 and 2 of the book "Topics in Optimal Transportation" by Cedric Villani.