A numerical method to solve the Stokes problem with a punctual force in source term
For researchers in computational fluid dynamics, this provides a way to handle singular forces while preserving numerical accuracy, though it is an incremental extension of existing techniques.
The paper presents a numerical method for solving the Stokes problem with a Dirac source term that maintains optimal finite-element convergence for any approximation order. The method is motivated by modeling active thin structures in viscous fluids.
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the knowledge of a fundamental solution to the associated operator over the whole space. This method is motivated by the modeling of the movement of active thin structures in a viscous fluid.