An inverse problem for slow viscous incompressible flows

摘要

This paper considers an inverse boundary value problem associated to the Stokes equations which goven the motion of slow viscous incompressible flows of fluids. 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. SThe 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 regulartization method with the choice of the regularization parameter based on the L-curve critierion. In addition, an investigation into the stability of the numerical solution has been made by adding a random small perturbation to the input data.