Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation
From MaRDI portal
Publication:2021080
DOI10.1016/j.cma.2020.113243zbMath1506.76097OpenAlexW2996909697WikidataQ114196916 ScholiaQ114196916MaRDI QIDQ2021080
Jan Papež, Martin Vohralík, Ulrich Rüde, Barbara I. Wohlmuth
Publication date: 26 April 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2020.113243
finite element methoda posteriori error estimateporous media flowmass balance\(p\)-robustnessiterative algebraic solver
Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)
Related Items
An adaptive \(hp\)-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor ⋮ Adaptive solution of linear systems of equations based on a posteriori error estimators ⋮ Estimating and localizing the algebraic and total numerical errors using flux reconstructions ⋮ Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria ⋮ Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality ⋮ Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations ⋮ A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior ⋮ Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem ⋮ A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types ⋮ Contractive local adaptive smoothing based on Dörfler's marking in a-posteriori-steered \(p\)-robust multigrid solvers ⋮ Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations ⋮ A-Posteriori-Steered $p$-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps ⋮ Quasi-Optimal Mesh Sequence Construction through Smoothed Adaptive Finite Element Methods ⋮ Adaptive inexact semismooth Newton methods for the contact problem between two membranes
Uses Software
Cites Work
- A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
- Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients
- On hybrid multigrid-Schwarz algorithms
- Optimal multilevel methods for graded bisection grids
- Compatible algorithms for coupled flow and transport
- A massively parallel solver for discrete Poisson-like problems
- An optimal Poincaré inequality for convex domains
- Adaptive inexact semismooth Newton methods for the contact problem between two membranes
- Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
- Inexact linear solvers for control volume discretizations in porous media
- A posteriori estimates for partial differential equations
- A framework for obtaining guaranteed error bounds for finite element approximations
- Equilibrated residual error estimates are \(p\)-robust
- An adaptive, multi-level method for elliptic boundary value problems
- A note on the Poincaré inequality for convex domains
- A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows
- 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
- A projection method for constructing a mass conservative velocity field
- On the abstract theory of additive and multiplicative Schwarz algorithms
- Adaptive error control for multigrid finite element methods
- A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations
- A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities
- An adaptive \(hp\)-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor
- A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types
- A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows
- Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers
- Finite element potentials
- Estimating and localizing the algebraic and total numerical errors using flux reconstructions
- Distribution of the discretization and algebraic error in numerical solution of partial differential equations
- Projections of velocity data for the compatibility with transport
- Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
- Mixed virtual element methods for general second order elliptic problems on polygonal meshes
- Gradient schemes: Generic tools for the numerical analysis of diffusion equations
- Stopping Criteria for Adaptive Finite Element Solvers
- Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
- An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow
- Iterative Methods for Linear Systems
- Multigrid Techniques
- 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
- Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods
- A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
- On the Discrete Poincaré–Friedrichs Inequalities for Nonconforming Approximations of the Sobolev Space H 1
- Comparison of multigrid algorithms for high‐order continuous finite element discretizations
- Multilevel Block Factorization Preconditioners
- An a posteriori error estimator for the Lame equation based on equilibrated fluxes
- Locally Conservative Fluxes for the Continuous Galerkin Method
- Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids
- Convergence and quasi-optimal complexity of a simple adaptive finite element method
- The approximation of the pressure by a mixed method in the simulation of miscible displacement
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- Local Mesh Refinement Multilevel Techniques
- Mixed and Hybrid Finite Element Methods
- Fully Adaptive Multigrid Methods
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- Explicit error bounds in a conforming finite element method
- Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly
- Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
- Fully Reliable Localized Error Control in the FEM
- A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
- Analysis of multilevel decomposition iterative methods for mixed finite element methods
- On the Implementation of Mixed Methods as Nonconforming Methods for Second- Order Elliptic Problems
- Uniform Convergence of Adaptive Multigrid Methods for Elliptic Problems and Maxwell's Equations
- A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with $p$-Robust Behavior
- Error estimates for a finite element solution of the diffusion equation based on composite norms
- 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
- Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations
- Performance and Scalability of Hierarchical Hybrid Multigrid Solvers for Stokes Systems
- Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations
- Equilibrated residual error estimator for edge elements
- Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements
- hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
- Spectral Element Methods on Simplicial Meshes
- Approximations in elasticity based on the concept of function space
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
