A posteriori algebraic error estimates and nonoverlapping domain decomposition in mixed formulations: energy coarse grid balancing, local mass conservation on each step, and line search - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2024

A posteriori algebraic error estimates and nonoverlapping domain decomposition in mixed formulations: energy coarse grid balancing, local mass conservation on each step, and line search

Résumé

We consider iterative algebraic solvers for the saddle-point mixed finite element discretizations of the model Darcy flow problem. We propose a posteriori error estimators of the algebraic error as well as a nonoverlapping domain decomposition algorithm. The estimators control the algebraic error from above and from below in a guaranteed and fully computable way. The distinctive feature of the domain decomposition algorithm is that it produces a locally mass conservative approximation on each iteration. Both the estimate and the algorithm rely on a coarse grid solver, a subdomain Neumann solver, and a subdomain Dirichlet solver. The algorithm also employs a line search to determine the optimal step size, leading to a Pythagoras formula for the algebraic error decrease in each iteration. Numerical experiments illustrate the theoretical developments and confirm the efficiency of the algebraic error estimates and of the domain decomposition algorithm.
Fichier principal
Vignette du fichier
DD_MFE.pdf (10.29 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04843665 , version 1 (17-12-2024)

Licence

Identifiants

  • HAL Id : hal-04843665 , version 1

Citer

Manuela Bastidas Olivares, Akram Beni Hamad, Martin Vohralík, Ivan Yotov. A posteriori algebraic error estimates and nonoverlapping domain decomposition in mixed formulations: energy coarse grid balancing, local mass conservation on each step, and line search. 2024. ⟨hal-04843665⟩

Collections

ENPC INRIA INRIA2
0 Consultations
0 Téléchargements

Partager

More