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We prove linear convergence for a new family of modified Dirichlet–Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin–Robin method. Such nonoverlapping domain decomposition methods are commonly employed for the parallelization of partial differential equation solvers. Convergence has been extensively studied for elliptic equations, but in the case of parabolic equations there are hardly any convergence results that are not relying on strong regularity assumptions. Hence, we construct a new framework for analyzing domain decomposition methods applied to quasilinear parabolic problems, based on fractional time derivatives and timedependent Steklov–Poincaré operators. The convergence analysis is conducted without assuming restrictive regularity assumptions on the solutions or the numerical iterates. We also prove that these continuous convergence results extend to the discrete case obtained when combining domain decompositions with spacetime finite elements.
Originalspråk  engelska 

Utgivare  arXiv.org 
Antal sidor  31 
DOI  
Status  Published  2023 
Ämnesklassifikation (UKÄ)
 Matematisk analys
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Utforska forskningsämnen för ”Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations”. Tillsammans bildar de ett unikt fingeravtryck.Projekt
 1 Avslutade

Nästa generations partitioneringsmetoder för tidsberoende PDEer
2020/01/01 → 2023/12/31
Projekt: Forskning