A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems
From MaRDI portal
Publication:1988111
DOI10.1016/j.cma.2019.05.014zbMath1441.65090arXiv1812.07972OpenAlexW2903671168WikidataQ127815168 ScholiaQ127815168MaRDI QIDQ1988111
Mark Ainsworth, Tomáv s Vejchodský
Publication date: 16 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.07972
finite element analysisflux reconstructionsingularly perturbed problemsrobust a posteriori error estimate
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
Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction ⋮ A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps ⋮ Primal-Dual Reduced Basis Methods for Convex Minimization Variational Problems: Robust True Solution a Posteriori Error Certification and Adaptive Greedy Algorithms ⋮ Adaptive analysis using scaled boundary finite element method in 3D ⋮ A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem ⋮ An efficient DWR-type a posteriori error bound of SDFEM for singularly perturbed convection-diffusion PDEs ⋮ Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction–diffusion problems ⋮ On error control at numerical solution of forth order elliptic equations with strongly discontinuous reaction coefficient
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids
- Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems
- A unified framework for a posteriori error estimation for the Stokes problem
- A posteriori estimates for partial differential equations
- A posteriori error estimators for convection-diffusion equations
- Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation
- Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues
- Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension
- Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes
- Estimating and localizing the algebraic and total numerical errors using flux reconstructions
- A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
- Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
- A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
- Guaranteed and robusta posteriorierror estimates for singularly perturbed reaction–diffusion problems
- Guaranteed energy error bounds for the Poisson equation using a flux-free approach: Solving the local problems in subdomains
- The self-equilibration of residuals and complementarya posteriori error estimates in the finite element method
- Error Estimate Procedure in the Finite Element Method and Applications
- Mixed and Hybrid Finite Element Methods
- Convergence of a finite element method based on the dual variational formulation
- Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems
- Explicit error bounds in a conforming finite element method
- A comparison of adaptive refinement techniques for elliptic problems
- A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Equilibrated residual error estimator for edge elements
- Approximations in elasticity based on the concept of function space
