Computing Bounds for Linear Functionals of Exact Weak Solutions to the Advection-Diffusion-Reaction Equation

DOI10.1137/S1064827503427121zbMath1082.65113MaRDI QIDQ4652345

No author found.

Publication date: 25 February 2005

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

finite element method local mesh refinement linear elliptic convection-diffusion-reaction equation one-sided error bounds

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Related Items (23)

Worst case error bounds for the solution of uncertain Poisson equations with mixed boundary conditions ⋮ Anisotropic mesh adaptation for continuous finite element discretization through mesh optimization via error sampling and synthesis ⋮ Guaranteed computable bounds on quantities of interest in finite element computations ⋮ An efficient method for computing local quantities of interest in elasticity based on finite element error estimation ⋮ 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 ⋮ Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ Guaranteed a-posteriori error estimation for semi-discrete solutions of parabolic problems based on elliptic reconstruction ⋮ A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation ⋮ Certified error bounds for uncertain elliptic equations ⋮ A posteriori goal-oriented bounds for the Poisson problem using potential and equilibrated flux reconstructions: application to the hybridizable discontinuous Galerkin method ⋮ Bounds for quantities of interest and adaptivity in the element-free Galerkin method ⋮ Exact Bounds for Linear Outputs of the Convection-Diffusion-Reaction Equation Using Flux-Free Error Estimates ⋮ Goal-oriented a posteriori error estimates for transport problems ⋮ A reduced basis method with exact-solution certificates for steady symmetric coercive equations ⋮ Strict upper and lower bounds for quantities of interest in static response sensitivity analysis ⋮ A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates ⋮ Bounds on outputs of the exact weak solution of the three-dimensional Stokes problem ⋮ Guaranteed energy error bounds for the Poisson equation using a flux-free approach: Solving the local problems in subdomains ⋮ 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 ⋮ Convergence of Anisotropic Mesh Adaptation via Metric Optimization

Uses Software

Triangle

This page was built for publication: Computing Bounds for Linear Functionals of Exact Weak Solutions to the Advection-Diffusion-Reaction Equation