Seminar for Applied Mathematics

output

19992022

most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing 2020 · math.NAShow all

6 papers · 2 filters

math.NA2020★ 15 cited

Exponential Convergence of $h p$ FEM for Spectral Fractional Diffusion in Polygons

Lehel Banjai, Jens M. Melenk, Christoph Schwab

For the spectral fractional diffusion operator of order $2 s \in (0, 2)$ in bounded, curvilinear polygonal domains $Ω$ we prove exponential convergence of two classes of $h p$ discreti…

math.NA2020★ 20 cited

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities

Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen +1

We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in $H^{1} (Ω)$ for weighted analytic function classes in certain polytopal domains $Ω$ , in space dimensio…

math.NA2020★ 5 cited

Second-order accurate TVD numerical methods for nonlocal nonlinear conservation laws

Ulrik Skre Fjordholm, Adrian Montgomery Ruf

We present a second-order accurate numerical method for a class of nonlocal nonlinear conservation laws called the "nonlocal pair-interaction model" which was recently introduced b…

math.NA2020★ 26 cited

Well-balanced finite volume schemes for nearly steady adiabatic flows

Luc Grosheintz-Laval, Roger Käppeli

We present well-balanced finite volume schemes designed to approximate the Euler equations with gravitation. They are based on a novel local steady state reconstruction. The scheme…

math.NA2020★ 35 cited

Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations

Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler +2

One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear parti…

math.NA2020★ 2 cited

Space-time discontinuous Galerkin approximation of acoustic waves with point singularities

Pratyuksh Bansal, Andrea Moiola, Ilaria Perugia +1

We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $Ω \subset R^{2}$ , possibly occupied by piecewise ho…