Innovative Approaches to the Numerical Approximation of PDEs

  • Stephan Dahlke

    Philipps-Universität, Marburg, Germany
  • Gitta Kutyniok

    Technische Universität Berlin, Germany
  • Ricardo H. Nochetto

    University of Maryland, College Park, USA
  • Rob Stevenson

    University of Amsterdam, Netherlands

Abstract

This workshop was about the numerical solution of PDEs for which classical approaches, such as the finite element method, are not well suited or need further (theoretical) underpinnings. A prominent example of PDEs for which classical methods are not well suited are PDEs posed in high space dimensions. New results on low rank tensor approximation for those problems were presented. Other presentations dealt with regularity of PDEs, the numerical solution of PDEs on surfaces, PDEs of fractional order, numerical solvers for PDEs that converge with exponential rates, and the application of deep neural networks for solving PDEs.

Cite this article

Stephan Dahlke, Gitta Kutyniok, Ricardo H. Nochetto, Rob Stevenson, Innovative Approaches to the Numerical Approximation of PDEs. Oberwolfach Rep. 16 (2019), no. 3, pp. 2473–2540

DOI 10.4171/OWR/2019/40