High-Order Numerical Approximation for Partial Differential Equations

Date: 6-10 February 2012

Venue: Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

Organizers: Alexey Chernov (HCM, University of Bonn), Christoph Schwab (ETH Zurich)

The aim of the workshop is to bring together the leading scientists and active young researchers working on High-Order Numerical Approximation for Partial Differential Equations and to initiate an intensive idea exchange between the research fields.

The main topics of the workshop include (but are not limited to) the theoretical and practical aspects of

  • Conforming hp-Finite Element and Spectral Methods
  • hp-Discontinuous Galerkin Finite Elements
  • Adaptive hp-Finite Elements
  • Isogeometric Analysis, Non-Uniform Rational B-Splines
  • Uncertainty Quantification and high-order methods for PDEs with random parameters
  • Computing with high-order non-standard basis functions

The use of high-order approximation methods is very effective in achieving high accuracy numerical simulations while keeping the number of unknowns moderate, in particular for piecewise smooth solutions of PDEs. The numerical and theoretical studies for this kind of methods began in the late 70s - early 80s. Since that time high-order discretization schemes are getting increasingly popular in many practical applications such as fluid dynamics, structural mechanics, electromagnetics, acoustics, etc., giving rise to new research directions requiring a new mathematical theory; in particular, the recently emerged and fast developing Isogeometric Methods and high-order methods of Uncertainty Quantification.