Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations

Monika Eisenmann, Eskil Hansen

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

Sammanfattning

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the p-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approximation theory for nonlinear semigroups.

Originalspråkengelska
Sidor (från-till)913-938
TidskriftNumerische Mathematik
Volym140
Nummer4
Tidigt onlinedatum2018 juli 7
DOI
StatusPublished - 2018 dec.

Ämnesklassifikation (UKÄ)

  • Beräkningsmatematik

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