Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems
DOI10.1515/jnma-2014-0074zbMath1351.65090OpenAlexW2402778897MaRDI QIDQ325813
Matthias Maier, Rolf Rannacher
Publication date: 11 October 2016
Published in: Journal of Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/jnma-2014-0074
finite element methodmesh adaptationgoal-oriented adaptivitya posteriori error estimationdual weighted residual methodelliptic diffusion problemsheterogeneous multiscale methodmodel adaptation
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
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- The \texttt{deal.II} library, version 8.4
- Variational localizations of the dual weighted residual estimator
- The heterogeneous multiscale methods
- Multi-scale computational homogenization: trends and challenges
- The variational multiscale method -- a paradigm for computational mechanics
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
- A note on homogenization of advection-diffusion problems with large expected drift
- Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements
- Multiscale finite element methods for nonlinear problems and their applications
- A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
- Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
- Analysis of the heterogeneous multiscale method for elliptic homogenization problems
- An optimal control approach to a posteriori error estimation in finite element methods
- Subgrid Upscaling and Mixed Multiscale Finite Elements
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- Homogenization and Two-Scale Convergence
- Two-scale FEM for homogenization problems
- A Posteriori Control of Modeling Errors and Discretization Errors
- A mixed multiscale finite element method for elliptic problems with oscillating coefficients
- Multigrid techniques for finite elements on locally refined meshes
- An Adaptive Multiscale Finite Element Method
- MultiScale Modeling of Physical Phenomena: Adaptive Control of Models
- Local Goal-Oriented Estimation of Modeling Error for Multi-Scale Modeling of Heterogeneous Elastic Materials
- On constitutive macro-variables for heterogeneous solids at finite strain
- A Posteriori Error Estimates for the Heterogeneous Multiscale Finite Element Method for Elliptic Homogenization Problems
- On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM
- Estimation of local model error and goal-oriented adaptive modeling of heterogeneous materials. II: A computational environment for adaptive modeling of heterogeneous elastic solids
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