Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems
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Publication:6052342
DOI10.1016/j.camwa.2023.07.008OpenAlexW4385317616MaRDI QIDQ6052342
Emmanuel Creusé, Zuqi Tang, Serge Nicaise
Publication date: 21 September 2023
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2023.07.008
Boundary value problems for second-order elliptic equations (35J25) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) 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)
Cites Work
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- Variational localizations of the dual weighted residual estimator
- Strict upper bounds of the error in calculated outputs of interest for plasticity problems
- An optimal Poincaré inequality for convex domains
- Strict upper error bounds on computed outputs of interest in computational structural mechanics
- Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems
- Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems
- A note on the Poincaré inequality for convex domains
- Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems
- Strict bounding of quantities of interest in computations based on domain decomposition
- On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
- Explicit-in-time goal-oriented adaptivity
- Quantifying discretization errors for soft tissue simulation in computer assisted surgery: a preliminary study
- Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors
- Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering
- A posteriori error estimates of goal-oriented adaptive finite element methods for nonlinear reaction-diffusion problems
- Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs
- A posteriori goal-oriented bounds for the Poisson problem using potential and equilibrated flux reconstructions: application to the hybridizable discontinuous Galerkin method
- Time-domain goal-oriented adaptivity using pseudo-dual error representations
- Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers
- Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
- Automated Goal-Oriented Error Control I: Stationary Variational Problems
- Guaranteed computable bounds on quantities of interest in finite element computations
- A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes
- New bounding techniques for goal-oriented error estimation applied to linear problems
- Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest
- A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
- Weighted Marking for Goal-oriented Adaptive Finite Element Methods
- An optimal control approach to a posteriori error estimation in finite element methods
- A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations
- A Goal-Oriented Adaptive Finite Element Method with Convergence Rates
- A safeguarded dual weighted residual method
- Singularities of Maxwell interface problems
- New development in freefem++
- A posteriorierror estimates for a nonconforming finite element discretization of the heat equation
- Goal-oriented error estimation and adaptivity for the finite element method
