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08/05/2023
A Modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes
We introduce a new numerical method for solving time-harmonic Maxwell's ...
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06/25/2023
High Order Morley Elements for Biharmonic Equations on Polytopal Partitions
This paper introduces an extension of the Morley element for approximati...
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05/15/2023
Generalized weak Galerkin finite element methods for second order elliptic problems
This article proposes and analyzes the generalized weak Galerkin (gWG) f...
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05/15/2023
Finite Expression Methods for Discovering Physical Laws from Data
Nonlinear dynamics is a pervasive phenomenon observed in various scienti...
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02/21/2023
Deep Learning via Neural Energy Descent
This paper proposes the Nerual Energy Descent (NED) via neural network e...
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02/13/2023
Generalized Weak Galerkin Finite Element Methods for Biharmonic Equations
The generalized weak Galerkin (gWG) finite element method is proposed an...
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01/28/2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Deep neural networks (DNNs) have seen tremendous success in many fields ...
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12/24/2022
An L^p-primal-dual finite element method for first-order transport problems
A new L^p-primal-dual weak Galerkin method (L^p-PDWG) with p>1 is propos...
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10/31/2022
Weak Galerkin methods based Morley elements on general polytopal partitions
A new weak Galerkin method based on the weak tangential derivative and w...
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10/30/2022
Curved Elements in Weak Galerkin Finite Element Methods
A mathematical analysis is established for the weak Galerkin finite elem...
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10/29/2022
Weak Galerkin Finite Element Methods for Quad-Curl Problems
This article introduces a weak Galerkin (WG) finite element method for q...
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08/02/2022
An L^p- Primal-Dual Weak Galerkin method for div-curl Systems
This paper presents a new L^p-primal-dual weak Galerkin (PDWG) finite el...
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04/11/2022
A parallel iterative procedure for weak Galerkin methods for second order elliptic problems
A parallelizable iterative procedure based on domain decomposition is pr...
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12/28/2021
Active Learning Based Sampling for High-Dimensional Nonlinear Partial Differential Equations
The deep-learning-based least squares method has shown successful result...
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12/13/2021
A Weak Galerkin Method for Elasticity Interface Problems
This article introduces a weak Galerkin (WG) finite element method for l...
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11/22/2021
An L^p- Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations
In this article, the authors present a new L^p- primal-dual weak Galerki...
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04/11/2021
Adaptive Learning on the Grids for Elliptic Hemivariational Inequalities
This paper introduces a deep learning method for solving an elliptic hem...
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01/13/2021
Reproducing Activation Function for Deep Learning
In this paper, we propose the reproducing activation function to improve...
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01/10/2021
A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions
This paper presents a numerical method for div-curl systems with normal ...
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12/15/2020
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
This paper proposes Friedrichs learning as a novel deep learning methodo...
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11/24/2020
Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems
A new primal-dual weak Galerkin (PDWG) finite element method is introduc...
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11/22/2020
A Modified Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form
A modified primal-dual weak Galerkin (M-PDWG) finite element method is d...
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10/27/2020
A New Primal-Dual Weak Galerkin Method for Elliptic Interface Problems with Low Regularity Assumptions
This article introduces a new primal-dual weak Galerkin (PDWG) finite el...
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07/07/2020
Structure Probing Neural Network Deflation
Deep learning is a powerful tool for solving nonlinear differential equa...
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06/25/2020
A simplified primal-dual weak Galerkin finite element method for Fokker-Planck type equations
A simplified primal-dual weak Galerkin (S-PDWG) finite element method is...
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04/28/2020
De Rham Complexes for Weak Galerkin Finite Element Spaces
Two de Rham complex sequences of the finite element spaces are introduce...
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01/19/2020
New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems
This article devises a new primal-dual weak Galerkin finite element meth...
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10/30/2019
A Primal-dual weak Galerkin finite element method for linear convection equations in non-divergence form
A new primal-dual weak Galerkin (PD-WG) finite element method was develo...
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10/30/2019
Primal-dual weak Galerkin finite element methods for linear convection equations in non-divergence form
A new primal-dual weak Galerkin (PD-WG) finite element method was develo...
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06/18/2019
A primal-dual finite element method for first-order transport problems
This article devises a new numerical method for first-order transport pr...
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06/18/2019
