Fitted norm preconditioners for the Hodge-Laplacian in mixed form

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F25%3A00642860" target="_blank" >RIV/68145535:_____/25:00642860 - isvavai.cz</a>
Result on the web
<a href="https://articles.math.cas.cz/10.21136/AM.2025.0185-25" target="_blank" >https://articles.math.cas.cz/10.21136/AM.2025.0185-25</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2025.0185-25" target="_blank" >10.21136/AM.2025.0185-25</a>

Result language
angličtina
Original language name
Fitted norm preconditioners for the Hodge-Laplacian in mixed form
Original language description
We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models. We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)