Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations.

In this paper, we investigate the application of the fading regularization method with the method of fundamental solutions (MFS) to the ill-posed Cauchy-Stokes problem. For both smooth and piecewise smooth two-dimensional geometries, we present a numerical reconstruction of the missing velocity and normal stress tensor on an inaccessible part of the boundary based on knowledge of over-prescribed noisy data acquired on the remaining accessible boundary part. Three numerical examples demonstrate the proposed numerical algorithm's accuracy, convergence, stability, and efficiency, as well as its ability to deblur the data. [ABSTRACT FROM AUTHOR]