An inverse Stokes problem using interior pressure data

An inverse boundary value problem associated to the Stokes equations in a domain of two dimensions is considered. This problem requires the determination of the unspecified surface fluid velocity, or one of its components, over a part of its boundary by introducing extra interior pressure measurements. The problem is discretised numerically using the boundary element method (BEM) and the resulting ill-conditioned system of linear algebraic equations is solved using the Tikhonov regularisation method, with the choice of the regularisation parameter based on the L-curve criterion. The numerical technique is validated for some test examples with known analytical solutions. The accuracy of the numerical solutions is checked by comparison with their corresponding exact values and an investigation into stability of the numerical solution is undertaken by the addition of random noise into the interior pressure measurements. It is shown that the BEM provides a stable numerical solution of the Stokes problem which converges to the exact solution as the magnitude of error in the interior data decreases.