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

• Published in: Numerical algorithms Vol. 96; no. 1; pp. 59 - 73
• Main Authors: Borachok, Ihor, Chapko, Roman, Johansson, B. Tomas
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2024; Springer Nature B.V
• Subjects: Algebra; Algorithms; Approximation; Boundary conditions; Boundary value problems; Computer Science; Integral equations; Numeric Computing; Numerical Analysis; Original Paper; Reynolds number; Theory of Computation; Thermal expansion; 65N80; Method of fundamental solutions; Dirichlet boundary condition; 76D07; 76M20; Rothe’s method; Unsteady Stokes problem; Rothes method
• ISSN: 1017-1398; 1572-9265; 1572-9265
• DOI: 10.1007/s11075-023-01639-1

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.