A posteriori error estimates for the time-dependent convection-diffusion-reaction equation and application to the finite volume methods
type: Dataset
contact point: Organization
  fn: CCSD
keyword: adaptive-algorithm
keyword: a-posteriori-error-estimates
keyword: parabolic-problems
keyword: convection--diffusion--reaction
keyword: theses
keyword: estimation-derreur-a-posteriori
keyword: methodes-de-volumes-finis
keyword: algorithme-adaptatif
keyword: finite-volume-methods
keyword: problemes-paraboliques
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
landing page: https://pastel.hal.science/pastel-00794392
description: We consider the time-dependent convection--diffusion--reaction equation. We derive a posteriori error estimates for the discretization of this equation by the cell-centered finite volume scheme in space and a backward Euler scheme in time. The estimates are established in the energy norm and they bound the error between the exact solution and a locally post processed approximate solution, based on H(div,Ω)-conforming diffusive and convective flux reconstructions, as well as an H¹₀(Ω)-conforming potential reconstruction. We propose an adaptive algorithm which ensures the control of the total error with respect to a user-defined relative precision by refining the meshes adaptively while equilibrating the time and space contributions to the error. We also present numerical experiments. Finally, we derive another a posteriori error estimate in the energy norm augmented by a dual norm of the time derivative and the skew symmetric part of the differential operator. The new estimate is robust in convective-dominated regimes and local-in-time and global-in-space lower bounds are also derived
identifier: NNT: 2012PEST1065
issued: 2026-05-14T04:13:59.912923
language: fr
modified: 2026-05-14T04:13:59.912930

A posteriori error estimates for the time-dependent convection-diffusion-reaction equation and application to the finite volume methods
type: Distribution
access URL: https://pastel.hal.science/pastel-00794392
format: HTML
issued: 2026-05-14T04:13:59.929125
modified: 2026-05-14T04:13:59.883933

test_moissonnage_selune
type: Agent