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06/14/2023
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
The numerical solution of differential equations using machine learning-...
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02/15/2023
A New Reduced Basis Method for Parabolic Equations Based on Single-Eigenvalue Acceleration
In this paper, we develop a new reduced basis (RB) method, named as Sing...
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08/09/2022
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Neural networks are universal function approximators which are known to ...
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07/05/2022
A sharp Korn's inequality for piecewise H^1 space and its application
In this paper, we revisit Korn's inequality for the piecewise H^1 space ...
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07/04/2022
An efficient iterative method for dynamical Ginzburg-Landau equations
In this paper, we propose a new finite element approach to simulate the ...
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07/02/2022
Generalized Korn's Inequalities for Piecewise H^2 Vector Fields
The purpose of this paper is to construct a new class of discrete genera...
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04/07/2021
Rademacher Complexity and Numerical Quadrature Analysis of Stable Neural Networks with Applications to Numerical PDEs
Methods for solving PDEs using neural networks have recently become a ve...
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03/16/2021
A new framework for the stability analysis of perturbed saddle-point problems and applications in poromechanics
This paper provides a new abstract stability result for perturbed saddle...
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01/24/2021
An Extended Galerkin analysis in finite element exterior calculus
For the Hodge–Laplace equation in finite element exterior calculus, we i...
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05/01/2020
An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
In this paper, we propose and analyze an abstract stabilized mixed finit...
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02/26/2020
An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor
This paper presents an extended Galerkin analysis for various Galerkin m...
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01/22/2020
Robust block preconditioners for poroelasticity
In this paper we study the linear systems arising from discretized poroe...
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10/14/2019
Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot's consolidation and multiple-network poroelasticity models
This work is concerned with the iterative solution of systems of quasi-s...
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08/22/2019