Boundary integral solvers for an evolutionary exterior Stokes problem

TL;DR

This paper develops and analyzes a boundary integral method for solving the time-dependent exterior Stokes problem, combining Galerkin semidiscretization and Convolution Quadrature, with convergence analysis and numerical validation.

Contribution

It introduces a full discretization scheme for the exterior transient Stokes problem using boundary integral methods, Galerkin semidiscretization, and Convolution Quadrature, with detailed convergence analysis.

Findings

Convergence estimates are established via Laplace domain analysis.

Numerical experiments validate the theoretical results.

The method effectively solves the exterior transient Stokes problem.

Abstract

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in the space variables and multistep Convolution Quadrature in time. Convergence estimates are based on a Laplace domain analysis, which translates into a detailed study of the exterior Brinkman problem. Some numerical experiments are provided.