Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations
DOI10.1007/s11075-021-01118-5zbMath1492.65328OpenAlexW2999898337MaRDI QIDQ2066207
Publication date: 13 January 2022
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/hal-02422851v4/file/PapVoh21.pdf
finite element methoda posteriori error estimateguaranteed upper boundalgebraic errorhierarchical splittingiterative algebraic solver
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Finite element methods applied to problems in fluid mechanics (76M10) 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)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An adaptive, multi-level method for elliptic boundary value problems
- Discrete \(p\)-robust \(\boldsymbol H(\mathrm{div})\)-liftings and a posteriori estimates for elliptic problems with \(H^{-1}\) source terms
- Stopping criteria for iterations in finite element methods
- On error estimation in the conjugate gradient method and why it works in finite precision computations
- Adaptive error control for multigrid finite element methods
- Multigrid in H(div) and H(curl)
- Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation
- Approximating the extreme Ritz values and upper bounds for the \(A\)-norm of the error in CG
- Estimating and localizing the algebraic and total numerical errors using flux reconstructions
- Stopping Criteria for Adaptive Finite Element Solvers
- Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
- Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\mathrm{curl}}$-Conforming High Order Finite Element Methods
- A Posteriori Error Estimates Based on Hierarchical Bases
- A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
- Local Mesh Refinement Multilevel Techniques
- Fully Adaptive Multigrid Methods
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- Explicit error bounds in a conforming finite element method
- Preconditioning in H(𝑑𝑖𝑣) and applications
- A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
- Mixed Finite Element Methods and Applications
- New development in freefem++
- Localization of the W-1,q norm for local a posteriori efficiency
- A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior
- Goal-oriented error control of the iterative solution of finite element equations
- Stable broken $H^1$ and $H(\mathrm {div})$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions
- TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
- Finite Elemente
This page was built for publication: Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations
