Exact Bounds for Linear Outputs of the Convection-Diffusion-Reaction Equation Using Flux-Free Error Estimates

DOI10.1007/978-3-540-79994-8_13zbMath1158.65344OpenAlexW4229813080MaRDI QIDQ3601907

Antonio Huerta, Pedro Díez, Núria Parés

Publication date: 12 February 2009

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-79994-8_13

zbMATH Keywords

domain decompositionerror estimationfinite elementpartition of unitygoal-oriented adaptivitylinear-functional outputsexact/guaranteed/strict boundssteady convection-reaction-diffusion equation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

• A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
• Subdomain-based flux-free a posteriori error estimators
• The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations
• Computing upper and lower bounds for the \(J\)-integral in two-dimensional linear elasticity
• Bounds of functional outputs for parabolic problems. I: Exact bounds of the discontinuous Galerkin time discretization
• Bounds of functional outputs for parabolic problems. II: Bounds of the exact solution
• 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
• Goal-oriented error estimation and adaptivity for the finite element method
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