Year: 2025
Type: article
Abstract: We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert spaces. We set the stage using the Finite Element Exterior Calculus and Nodal Auxiliary Space Preconditioning. This framework provides a systematic way to derive explicit residual estimators and estimators based on local problems which are upper and lower bounds of the true error. We show the applications to discretizations of curl-curl, grad-div, Hodge Laplacian problems, and linear elasticity. For singularly perturbed H ( curl ) H({\operatorname {curl}}) and H ( div ) H({\operatorname {div}}) problems, we also obtain novel parameter-independent error estimators. The only ingredients needed are: well-posedness of the problem and the existence of regular decomposition on continuous level.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4141
Authors: Yuwen Li, Ludmil Zikatanov
Institutions: Zhejiang University, Pennsylvania State University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4413467307