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Numerical Algorithms

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14.08.2023 | Original Paper

Rothe’s method in combination with a fundamental sequences method for the nonstationary Stokes problem

verfasst von: Ihor Borachok, Roman Chapko, B. Tomas Johansson

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

Rothe’s method combined with a fundamental sequences method is considered for the numerical solution of the nonstationary (unsteady) homogeneous Stokes problem in two-dimensional doubly connected domains. The Stokes system is reduced, using Rothe’s method, to a sequence of stationary inhomogeneous problems with a known sequence of fundamental solutions. The stationary problems are discretized by a fundamental sequences method; this means searching for the solution as a linear combination of elements of the fundamental sequence and matching the given boundary conditions in order to find the coefficients in the expansion of the solution. No additional reduction of the inhomogeneous problems is needed, making it an efficient method and different from standard strategies of the method of fundamental solutions. Results of numerical experiments are given, and these confirm the applicability of the proposed approach.

Vorheriger Artikel Jacobi spectral projection methods for Fredholm integral equations of the first kind

Nächster Artikel The nonsmooth Newton’s method for the horizontal nonlinear complementarity problem

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Titel: Rothe’s method in combination with a fundamental sequences method for the nonstationary Stokes problem
verfasst von: Ihor Borachok
Roman Chapko
B. Tomas Johansson
Publikationsdatum: 14.08.2023
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01639-1

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