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

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Abstract

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.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • Technical University of Berlin
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Beräkningsmatematik

Nyckelord

Originalspråkengelska
Sidor (från-till)913-938
TidskriftNumerische Mathematik
Volym140
Utgivningsnummer4
Tidigt onlinedatum2018 jul 7
StatusPublished - 2018 dec
PublikationskategoriForskning
Peer review utfördJa