Boundary element two-dimensional solution of an inverse Stokes problem

This paper considers an inverse boundary value problem associated to the Stokes equations. The determination of the under-specified boundary values of the normal fluid velocity is made possible by utilising within the analysis additional pressure measurements, which are available from elsewhere on the boundary. The inverse boundary value Stokes problem has been numerically discretised using a boundary element method (BEM). Then the resulting ill-conditioned system of linear algebraic equations solved in a circular domain using the Tikhonov regularisation method with the choice of the regularisation parameter based on the L-curve criterion. In addition, an investigation into the stability of the numerical solution has been made by adding a random small perturbation to the input boundary data.