142 citations · 696 across the 46 of their papers we have counts for
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Exponential Convergence of FEM for Spectral Fractional Diffusion in Polygons
Lehel Banjai, Jens M. Melenk, Christoph Schwab
For the spectral fractional diffusion operator of order in bounded, curvilinear polygonal domains we prove exponential convergence of two classes of discreti…
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 for weighted analytic function classes in certain polytopal domains , in space dimensio…
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks
M. Longo, S. Mishra, T. K. Rusch +1
We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps…
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions
V. Kazeev, I. Oseledets, M. Rakhuba +1
Homogenization in terms of multiscale limits transforms a multiscale problem with asymptotically separated microscales posed on a physical domain int…
Analytic regularity for the incompressible Navier-Stokes equations in polygons
Carlo Marcati, Christoph Schwab
In a plane polygon with straight sides, we prove analytic regularity of the Leray-Hopf solution of the stationary, viscous, and incompressible Navier-Stokes equations. We assum…
-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
Lehel Banjai, Jens M. Melenk, Christoph Schwab
In bounded, polygonal domains with Lipschitz boundary consisting of a finite number of Jordan curves admitting analytic parametrizations, we ana…