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07/21/2023
Weighted analytic regularity for the integral fractional Laplacian in polyhedra
On polytopal domains in ℝ^3, we prove weighted analytic regularity of so...
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09/23/2022
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons
We prove exponential convergence in the energy norm of hp finite element...
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04/08/2022
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
We prove weighted analytic regularity for the solution of the integral f...
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12/15/2021
Weighted analytic regularity for the integral fractional Laplacian in polygons
We prove weighted analytic regularity of solutions to the Dirichlet prob...
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12/15/2021
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations
We construct deep operator networks (ONets) between infinite-dimensional...
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10/23/2020
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities
We prove exponential expressivity with stable ReLU Neural Networks (ReLU...
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10/14/2020
Low rank tensor approximation of singularly perturbed partial differential equations in one dimension
We derive rank bounds on the quantized tensor train (QTT) compressed app...
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06/18/2020
p- and hp- virtual elements for the Stokes problem
We analyse the p- and hp-versions of the virtual element method (VEM) fo...
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04/23/2020
Analytic regularity for the incompressible Navier-Stokes equations in polygons
In a plane polygon P with straight sides, we prove analytic regularity o...
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12/17/2019
Tensor Rank bounds for Point Singularities in R^3
We analyze rates of approximation by quantized, tensor-structured repres...
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12/16/2019