Error estimates for discrete generalized FEMs with locally optimal spectral approximations

DOI10.1090/mcom/3755OpenAlexW4280579790WikidataQ114094303 ScholiaQ114094303MaRDI QIDQ5103751

Chupeng Ma, Robert Scheichl

Publication date: 8 September 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.09988

zbMATH Keywords

finite element methodselliptic problemseigenvalue problems

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (4)

Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems ⋮ Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations ⋮ Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations ⋮ A relaxed localized trust-region reduced basis approach for optimization of multiscale problems

Cites Work

• Unnamed Item
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• Generalized multiscale finite element methods (GMsFEM)
• A multiscale finite element method for elliptic problems in composite materials and porous media
• Elliptic partial differential equations of second order
• Multiscale-spectral GFEM and optimal oversampling
• Randomized Oversampling for Generalized Multiscale Finite Element Methods
• Machine Computation Using the Exponentially Convergent Multiscale Spectral Generalized Finite Element Method
• Optimal Local Approximation Spaces for Generalized Finite Element Methods with Application to Multiscale Problems
• Local energy estimates for the finite element method on sharply varying grids
• Analysis of the heterogeneous multiscale method for elliptic homogenization problems
• Localization of elliptic multiscale problems
• Multiscale Finite Element Methods
• THE PARTITION OF UNITY METHOD
• A mixed multiscale finite element method for elliptic problems with oscillating coefficients
• Mixed Finite Element Methods and Applications
• Randomized Sampling for Basis Function Construction in Generalized Finite Element Methods
• Mixed Generalized Multiscale Finite Element Methods and Applications
• A survey of direct methods for sparse linear systems
• Novel Design and Analysis of Generalized Finite Element Methods Based on Locally Optimal Spectral Approximations

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