Cover Image

Neural enrichment finite element method: A hybrid framework for problems with strong oscillations or interface problems

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Guo, Shihan, Richter, Thomas
Format:	Preprint
Published:	2026
Subjects:	Numerical Analysis 65M60, 65N15, 68T07
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Subspace method based on neural networks for eigenvalue problems
by: Dai, Xiaoying, et al.
Published: (2024)

A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
by: Cao, Jiachuan, et al.
Published: (2026)

A neuron-wise subspace correction method for the finite neuron method
by: Park, Jongho, et al.
Published: (2022)

An $r$-adaptive finite element method using neural networks for parametric self-adjoint elliptic problem
by: Aballay, Danilo, et al.
Published: (2025)

Data-Free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs
by: Lee, Jinsil, et al.
Published: (2025)

FieldTNN-based machine learning method for Maxwell eigenvalue problems
by: Jiang, Jiantao, et al.
Published: (2024)

An Eulerian finite element method for the linearized Navier--Stokes problem in an evolving domain
by: Neilan, Michael, et al.
Published: (2023)

Energy norm error estimates of a hybrid high-order method for the linear parabolic integro-differential equations on general meshes
by: Mohapatra, Achyuta Ranjan Dutta
Published: (2026)

Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
by: Franck, Emmanuel, et al.
Published: (2025)

Anisotropic hp space-time adaptivity and goal-oriented error control for convection-dominated problems
by: Margenberg, Nils, et al.
Published: (2026)

Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method
by: Zhang, Jiansong, et al.
Published: (2025)

Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum
by: Boon, Wietse M., et al.
Published: (2024)

Prediction of discretization of online GMsFEM using deep learning for Richards equation
by: Spiridonov, Denis, et al.
Published: (2024)

A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian
by: Barker, Mary, et al.
Published: (2022)

Neural Network Localized Orthogonal Decomposition for Numerical Homogenization of Diffusion Operators with Random Coefficients
by: Kröpfl, Fabian, et al.
Published: (2025)

Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains
by: Ta, Thi Thanh Mai, et al.
Published: (2025)

A unified immersed finite element error analysis for one-dimensional interface problems
by: Adjerid, Slimane, et al.
Published: (2023)

A posteriori analysis of neural network approximations
by: Führer, Thomas, et al.
Published: (2025)

Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
by: Ren, Jingze, et al.
Published: (2026)

Discontinuous Galerkin finite element operator network for solving non-smooth PDEs
by: Chawla, Kapil, et al.
Published: (2026)

Expression Rates of Neural Operators for Linear Elliptic PDEs in Polytopes
by: Marcati, Carlo, et al.
Published: (2024)

Discontinuous hybrid neural networks for the one-dimensional partial differential equations
by: Wang, Xiaoyu, et al.
Published: (2025)

A uniform and pressure-robust enriched Galerkin method for the Brinkman equations
by: Lee, Seulip, et al.
Published: (2023)

Improved a priori error estimates for a space-time finite element method for parabolic problems
by: Ta, Thi Thanh Mai, et al.
Published: (2025)

Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients
by: Khan, Arbaz, et al.
Published: (2025)

Optimal $L^2$ error estimates of mass- and energy-conserved FE schemes for a nonlinear Schrödinger-type system
by: Zhang, Zhuoyue, et al.
Published: (2023)

An efficient predictor-corrector approach with orthogonal spline collocation finite element technique for FitzHugh-Nagumo problem
by: Ngondiep, Eric
Published: (2026)

A stabilized nonconforming finite element method for the surface biharmonic problem
by: Wu, Shuonan, et al.
Published: (2024)

Regularization effect of noise on fully discrete approximation for stochastic reaction-diffusion equation near sharp interface limit
by: Cui, Jianbo
Published: (2023)

A framework of discontinuous Galerkin neural networks for iteratively approximating residuals
by: Yuan, Long, et al.
Published: (2025)

Stochastic Galerkin methods for linear stability analysis of systems with parametric uncertainty
by: Sousedík, Bedřich, et al.
Published: (2022)

Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)

A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems
by: Roth, Julian, et al.
Published: (2023)

Divergence-free decoupled finite element methods for incompressible flow problems
by: John, Volker, et al.
Published: (2025)

Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models
by: Ankur, et al.
Published: (2024)

Superclosenes error estimates for the div least-squares finite element method on elliptic problems
by: Chen, Gang, et al.
Published: (2024)

Multiscale Neural Networks for Approximating Green's Functions
by: Hao, Wenrui, et al.
Published: (2024)

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
by: Nguyen, Quang Huy, et al.
Published: (2025)

A Taylor-Hood finite element method for the surface Stokes problem without penalization
by: Demlow, Alan, et al.
Published: (2025)

The Neural Approximated Virtual Element Method for Elasticity Problems
by: Berrone, Stefano, et al.
Published: (2025)