Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions

DOI10.1137/20M1352922zbMath1473.65296arXiv2007.07418WikidataQ114074178 ScholiaQ114074178MaRDI QIDQ5006464

Yixuan Wang, Yi-Fan Chen, Thomas Yizhao Hou

Publication date: 16 August 2021

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.07418

zbMATH Keywords

adaptive methodexponential convergenceoversamplingmultiscale PDEsedge basis functionenergy orthogonal decomposition

Mathematics Subject Classification ID

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) Connections of harmonic functions with differential equations in two dimensions (31A35)

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An edge multiscale interior penalty discontinuous Galerkin method for heterogeneous Helmholtz problems with large varying wavenumber ⋮ Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data ⋮ An MsFEM Approach Enriched Using Legendre Polynomials ⋮ Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited ⋮ Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations ⋮ Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations ⋮ Optimal Local Approximation Spaces for Parabolic Problems ⋮ Super-localization of elliptic multiscale problems

Cites Work

• Unnamed Item
• Unnamed Item
• Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients
• Generalized multiscale finite element methods (GMsFEM)
• Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast
• An introduction to Sobolev spaces and interpolation spaces
• The variational multiscale method -- a paradigm for computational mechanics
• A multiscale finite element method for elliptic problems in composite materials and porous media
• The partition of unity finite element method: basic theory and applications
• Deriving upwinding, mass lumping and selective reduced integration by residual-free bubbles
• On \(n\)-widths for elliptic problems
• Bubble functions prompt unusual stabilized finite element methods.
• Elliptic partial differential equations of second order
• Multiscale-spectral GFEM and optimal oversampling
• Edge multiscale methods for elliptic problems with heterogeneous coefficients
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method
• 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
• Randomized Local Model Order Reduction
• An analysis of a class of variational multiscale methods based on subspace decomposition
• Localization of elliptic multiscale problems
• Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
• Multiscale Finite Element Methods
• Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
• CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS
• Wavelet-Based Numerical Homogenization
• Can a finite element method perform arbitrarily badly?
• Convergence of a Nonconforming Multiscale Finite Element Method
• Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
• Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods
• On the Convergence Rates of GMsFEMs for Heterogeneous Elliptic Problems Without Oversampling Techniques

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