Guaranteed computable bounds on quantities of interest in finite element computations
From MaRDI portal
Publication:2894972
DOI10.1002/nme.3276zbMath1242.65232OpenAlexW1667557491MaRDI QIDQ2894972
Richard Rankin, Mark Ainsworth
Publication date: 2 July 2012
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.3276
Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items (19)
An estimation of point-wise approximation error using the set of numerical solutions ⋮ Goal-oriented a posteriori error estimation for the biharmonic problem based on an equilibrated moment tensor ⋮ Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information ⋮ Orthogonality constrained gradient reconstruction for superconvergent linear functionals ⋮ Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and parabolic problems ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ A goal-oriented anisotropic \(hp\)-mesh adaptation method for linear convection-diffusion-reaction problems ⋮ Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM ⋮ Adaptive reduced basis finite element heterogeneous multiscale method ⋮ Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems ⋮ Quantifying discretization errors for soft tissue simulation in computer assisted surgery: a preliminary study ⋮ An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations ⋮ A posteriori goal-oriented bounds for the Poisson problem using potential and equilibrated flux reconstructions: application to the hybridizable discontinuous Galerkin method ⋮ Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm ⋮ NCP Function--Based Dual Weighted Residual Error Estimators for Signorini's Problem ⋮ Two-Side a Posteriori Error Estimates for the Dual-Weighted Residual Method ⋮ On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates ⋮ Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers ⋮ A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- An optimal Poincaré inequality for convex domains
- Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method
- A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints
- A framework for obtaining guaranteed error bounds for finite element approximations
- Reliable approximation of weight factors entering residual-based error bounds for FE-discretisa\-tions
- On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
- Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals
- The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations
- Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- An optimal control approach to a posteriori error estimation in finite element methods
- A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
- Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity
- Exact Bounds for Linear Outputs of the Advection-Diffusion-Reaction Equation Using Flux-Free Error Estimates
- Bounds for quantities of interest and adaptivity in the element-free Galerkin method
- A safeguarded dual weighted residual method
- Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints
- Guaranteed energy error bounds for the Poisson equation using a flux-free approach: Solving the local problems in subdomains
- A posteriorierror estimation and anisotropy detection with the dual-weighted residual method
- Computing Bounds for Linear Functionals of Exact Weak Solutions to the Advection-Diffusion-Reaction Equation
- Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson's Equation
- Anisotropic mesh refinement for discontinuous Galerkin methods in two‐dimensional aerodynamic flow simulations
- Goal-oriented error estimation and adaptivity for the finite element method
- A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem
This page was built for publication: Guaranteed computable bounds on quantities of interest in finite element computations
