Approximation of multi-scale elliptic problems using patches of finite elements.

DOI10.1016/j.crma.2003.09.029zbMath1036.65090OpenAlexW1973665814WikidataQ59241760 ScholiaQ59241760MaRDI QIDQ1420161

Jacques Rappaz, Joël Wagner, Roland Glowinski, Jiwen He

Publication date: 28 January 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.09.029

zbMATH Keywords

convergencefinite elementsnumerical examplesdomain decompositionPoisson equationfast adaptive composite grid methodmultilevel methodelliptic problems multi-scale data

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (12)

A multi-domain method for solving numerically multi-scale elliptic problems ⋮ A Nitsche hybrid multiscale method with non-matching grids ⋮ Accelerating the method of finite element patches using approximately harmonic functions ⋮ Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media ⋮ Numerical zoom for multiscale problems with an application to nuclear waste disposal ⋮ On the use of XFEM within the Arlequin framework for the simulation of crack propagation ⋮ A mortar element approach on overlapping non-nested grids: application to eddy current non-destructive testing ⋮ An overlapping mortar element approach to coupled magneto-mechanical problems ⋮ Numerical zoom for advection diffusion problems with localized multiscales ⋮ An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials ⋮ Finite element approximation of multi-scale elliptic problems using patches of elements ⋮ A two-grids/projection algorithm for obstacle problems

Uses Software

• FreeFem++

Cites Work

• Finite element approximation of multi-scale elliptic problems using patches of elements
• A Posteriori Error Estimates Based on Hierarchical Bases
• The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations
• Convergence Estimates for Product Iterative Methods with Applications to Domain Decomposition
• Some remarks on the constant in the strengthened CBS inequality: Estimate for hierarchical finite element discretizations of elasticity problems
• The Mortar Element Method with Overlapping Subdomains

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