Modified Neumann-Neumann methods for semi- and quasilinear elliptic equations

Forskningsoutput: Working paper/PreprintPreprint (i preprint-arkiv)

Sammanfattning

The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain quasilinear equations. We therefore propose two modified Neumann--Neumann methods that have better convergence properties and require less computations. We provide numerical results that show the advantages of these methods when applied to both semilinear and quasilinear equations. We also prove linear convergence with mesh-independent error reduction under certain assumptions on the equation. The analysis is carried out on general Lipschitz domains and relies on the theory of nonlinear Steklov--Poincaré operators.
Originalspråkengelska
UtgivarearXiv.org
Sidor1-22
Antal sidor22
DOI
StatusPublished - 2023 dec. 19

Ämnesklassifikation (UKÄ)

  • Matematisk analys

Fingeravtryck

Utforska forskningsämnen för ”Modified Neumann-Neumann methods for semi- and quasilinear elliptic equations”. Tillsammans bildar de ett unikt fingeravtryck.

Citera det här