Abstract
A large class of two-dimensional elliptic boundary value problems in acoustics, elasticity as well as hydrodynamics can be reduced to systems of boundary integral equations of the first kind with logarithmic singularities. This paper concerns in particular the stability analysis of the finite element method for treating such a class of integral equations. It is shown that an optimal choice of the mesh size can be made so that one may obtain an asymptotic optimal rate of convergence for the approximate solutions. The results here are in consistance with those obtained by the Tikhonov regularization procedure for improperly posed problems.
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