Rothe’s method in combination with a fundamental sequences method for the nonstationary Stokes problem - Borachok, Ihor; Chapko, Roman; Johansson, B. Tomas (Numerical algorithms, 2024)
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.