Oberwolfach Reports


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Volume 16, Issue 3, 2019, pp. 2473–2540
DOI: 10.4171/OWR/2019/40

Published online: 2020-09-09

Innovative Approaches to the Numerical Approximation of PDEs

Stephan Dahlke[1], Gitta Kutyniok[2], Ricardo H. Nochetto[3] and Rob Stevenson[4]

(1) Philipps-Universit├Ąt, Marburg, Germany
(2) Technische Universit├Ąt Berlin, Germany
(3) University of Maryland, College Park, USA
(4) University of Amsterdam, Netherlands

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.

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Dahlke Stephan, Kutyniok Gitta, Nochetto Ricardo, Stevenson Rob: Innovative Approaches to the Numerical Approximation of PDEs. Oberwolfach Rep. 16 (2019), 2473-2540. doi: 10.4171/OWR/2019/40