Year: 2021
Type: preprint
Abstract: Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local errors of a particular numerical solution. In this paper, we focus on a particular class of domain decomposition methods (DDM), which are among the most efficient numerical methods for solving PDEs. We adapt functional type a posteriori error estimates and construct a special form of error majorant which allows efficient error control of approximations computed via these DDM by performing only subdomain-wise computations. The presented guaranteed error bounds use an extended set of admissible fluxes which arise naturally in DDM.
Source: arXiv (Cornell University)
Authors: Kraus, Johannes, Repin, Sergey
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226449274