Boundary integral solvers for an evolutionary exterior Stokes problem
This work provides a rigorous numerical framework for solving time-dependent Stokes problems in exterior domains, which is important for applications in fluid dynamics but represents an incremental advance over existing boundary integral methods.
The paper develops a full discretization for the exterior transient Stokes problem using boundary integral methods and Convolution Quadrature, providing convergence estimates via Laplace domain analysis. Numerical experiments confirm the theoretical results.
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.