Exponentially convergent multiscale finite element method

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients
On best rank \(n\) matrix approximations
Sparse operator compression of higher-order elliptic operators with rough coefficients
The variational multiscale method -- a paradigm for computational mechanics
A multiscale finite element method for elliptic problems in composite materials and porous media
On \(n\)-widths for elliptic problems
Constraint energy minimizing generalized multiscale finite element method
Multiscale-spectral GFEM and optimal oversampling
Edge multiscale methods for elliptic problems with heterogeneous coefficients
Error estimates for a two-dimensional special finite element method based on component mode synthesis
Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures
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
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
The heterogeneous multiscale method
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
Metric-based upscaling
A special finite element method based on component mode synthesis
Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
Can a finite element method perform arbitrarily badly?
Convergence of a Nonconforming Multiscale Finite Element Method
Approximate Separability of the Green's Function of the Helmholtz Equation in the High Frequency Limit
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
Multiscale Elliptic PDE Upscaling and Function Approximation via Subsampled Data
Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
Error estimates for discrete generalized FEMs with locally optimal spectral approximations
Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods
For Most Frequencies, Strong Trapping Has a Weak Effect in Frequency‐Domain Scattering
On the Convergence Rates of GMsFEMs for Heterogeneous Elliptic Problems Without Oversampling Techniques
Bayesian Numerical Homogenization
Oversampling for the Multiscale Finite Element Method
The Mathematical Theory of Finite Element Methods
Optimal Local Approximation Spaces for Parabolic Problems
Super-localization of elliptic multiscale problems
Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems
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

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