A variational approach to splitting schemes, with applications to domain decomposition integrators

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A variational approach to splitting schemes, with applications to domain decomposition integrators. / Eisenmann, Monika; Hansen, Eskil.

I: Mathematics of Computation, 27.02.2019.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - A variational approach to splitting schemes, with applications to domain decomposition integrators

AU - Eisenmann, Monika

AU - Hansen, Eskil

PY - 2019/2/27

Y1 - 2019/2/27

N2 - Nonlinear parabolic equations are frequently encountered in applications andapproximating their solutions require large scale computations. In order toobtain efficient numerical approximations, it is crucial to design and analyzeschemes that can be implemented on parallel and distributed hardware. To thisend, we introduce a general framework of non-autonomous, inhomogeneousevolution equations in a variational setting, and show convergence of the sumoperator splitting scheme. We exemplify the usage to a p-Laplacian typeproblem with a possibly time depending domain decomposition.

AB - Nonlinear parabolic equations are frequently encountered in applications andapproximating their solutions require large scale computations. In order toobtain efficient numerical approximations, it is crucial to design and analyzeschemes that can be implemented on parallel and distributed hardware. To thisend, we introduce a general framework of non-autonomous, inhomogeneousevolution equations in a variational setting, and show convergence of the sumoperator splitting scheme. We exemplify the usage to a p-Laplacian typeproblem with a possibly time depending domain decomposition.

KW - Nonlinear evolution problem

KW - monotone operator

KW - operator splitting

KW - convergence

KW - domain decomposition

M3 - Article

JO - Mathematics of Computation

T2 - Mathematics of Computation

JF - Mathematics of Computation

SN - 1088-6842

ER -