Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data
DOI10.1137/20M1372214zbMath1482.65212arXiv2010.04199OpenAlexW4214553548WikidataQ114074147 ScholiaQ114074147MaRDI QIDQ5064414
Yi-Fan Chen, Thomas Yizhao Hou
Publication date: 15 March 2022
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.04199
localizationexponential decayfunction approximationmultiscale PDEsnumerical upscalingsubsampled data
Numerical computation using splines (65D07) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Theoretical approximation in context of PDEs (35A35)
Related Items (2)
Cites Work
- Unnamed Item
- Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients
- Sparse operator compression of higher-order elliptic operators with rough coefficients
- Weighted nonlocal Laplacian on interpolation from sparse data
- Constraint energy minimizing generalized multiscale finite element method
- Efficient implementation of the localized orthogonal decomposition method
- Properly-weighted graph Laplacian for semi-supervised learning
- Edge multiscale methods for elliptic problems with heterogeneous coefficients
- Function approximation via the subsampled Poincaré inequality
- Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
- Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast
- Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
- Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
- An analysis of a class of variational multiscale methods based on subspace decomposition
- Localization of elliptic multiscale problems
- Metric-based upscaling
- Elliptic Partial Differential Equations of Second Order
- Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
- Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions
- Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
- A High-Order Approach to Elliptic Multiscale Problems with General Unstructured Coefficients
- Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions
- Consistency of Lipschitz Learning with Infinite Unlabeled Data and Finite Labeled Data
- On the Convergence Rates of GMsFEMs for Heterogeneous Elliptic Problems Without Oversampling Techniques
- Analysis of $p$-Laplacian Regularization in Semisupervised Learning
- Bayesian Numerical Homogenization
- Oversampling for the Multiscale Finite Element Method
- Scattered Data Approximation
This page was built for publication: Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data
