01.07.2013

Luka Grubišić

University of Zagreb

Luka Grubišić

17.06.2013

Professor Klaus Boehmer

University of Marburg

Title: A Convergence Theory for Mesh-free Methods for a Nonlinear Second Order Elliptic Equation

Abstract: This lecture is an appetizer for my two books in OUP: Numerical Methods for Nonlinear Elliptic Differential Equations, A Synopsis, Numerical Methods for Bifurcation and Center Manifolds in Nonlinear Elliptic and Parabolic Differential Equations, 2010 and 2014. We extend for the first time the linear discretization theory of Schaback, developed for meshfree methods, to nonlinear operator equations, relying heavily on methods of Bohmer, Vol I. There is no restriction to elliptic problems nor to symmetric numerical methods like Galerkin techniques. Trial spaces can be arbitrary, but have to approximate the solution well, and testing can be weak or strong. We present Galerkin techniques as an example. On the downside, stability is not easy to prove for special applications, and numerical methods have to be formulated as optimization problems. Results of this discretization theory cover error bounds and convergence rates. As an example we present the meshless method for some nonlinear elliptic problems of second order. Numerical examples are added for illustration.

 

11.06.2013 to 13.06.2013

Annick Sartenaer

Facultes Universitaires N.-D. de la Paix

Annick Sartenaer

13.05.2013 to 17.05.2013

Laurence Halpern

University of Paris

Laurence Halpern

details to be finalised

13.05.2013 to 16.05.2013

Giovanni Samaey

KU Leuven

Giovanni Samaey

15.05.2013

Yuri Nesterov

CORE, UCL, Belgium

Yuri Nesterov

Title: Dual Methods for minimizing functions with bounded variation

Venue: JCMB 6206, King's Buildings, University of Edinburgh, on May 15th, 2013 @ 15:30

Abstract: We propose a new approach for justifying complexity bounds for dual optimization methods. Dual problems often have very big or unbounded size of the optimal solutions. This makes impossible to apply to the complexity analysis of corresponding schemes the standard framework. In this talk wepropose new methods, which can work with unbounded feasible sets. All these methods are primal-dual: they generate both primal and dual solutions with required accuracy/feasibility guarantees. This is a joint work with A. Gasnikov (IITP, Moscow)
 

30.04.2013 to 05.05.2013

Stephen Wright

University of Wisconsin-Madison

Stephen Wright

02.05.2013 to 03.05.2013

Peter Coveney

UCL

Peter Coveney

06.03.2013 to 07.03.2013

Han Wang

Freie Universitat Berlin

Han Wang

Pages