Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations
Research output: Working paper
Abstract
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them wellsuited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. 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 pLaplace 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.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Number of pages  21 
State  Submitted  2017 
Bibliographic note
Journal tba