A-Posteriori-Steered $p$-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps
DOI10.1137/20M1349503zbMath1486.65280OpenAlexW3010405962MaRDI QIDQ4997353
Jan Papež, Ani Miraçi, Martin Vohralík
Publication date: 29 June 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m1349503
multigrid methoda posteriori error estimateoptimal step-sizes\(p\)-robustnessstable decompositionerror representation formula
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Iterative numerical methods for linear systems (65F10) Second-order elliptic equations (35J15) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
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- Adaptive refinement for arbitrary finite-element spaces with hierarchical bases
- The hierarchical basis multigrid method
- Line relaxation for spectral multigrid methods
- Domain decomposition preconditioners for the spectral collocation method
- Additive Schwarz methods for the \(p\)-version finite element method
- Robust multigrid methods for nonsmooth coefficient elliptic linear systems
- \(V\)-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes
- Preconditioned minimal residual methods for Chebyshev spectral calculations
- Theory and practice of finite elements.
- Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation
- Adaptive solution of linear systems of equations based on a posteriori error estimators
- Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems
- Optimizing the number of multigrid cycles in the full multigrid algorithm
- Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods
- Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
- Comparison of multigrid algorithms for high‐order continuous finite element discretizations
- Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids
- New Convergence Estimates for Multigrid Algorithms
- Iterative Methods by Space Decomposition and Subspace Correction
- On the poisson equation with intersecting interfaces
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- Error Estimates for Adaptive Finite Element Computations
- The Construction of Preconditioners for Elliptic Problems by Substructuring. I
- A Convergent Adaptive Algorithm for Poisson’s Equation
- A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior
- Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements
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