AN APPROXIMATE METHOD ON NONEQUIDISTANT PARTITIONS FOR DOUBLE-LAYER POTENTIAL EQUATION

A quadrature method for double layer potential equations with continuo us coefficients on piecewise smooth curves is studied. The underlying grids are supposed to be locally non-equidistant. Such grids occur for instance in adaptive methods. Necessary and sufficient conditions for stability of the method are given in terms of invertibility of some w ell-defined model operators. These operators belong to an operator alg ebra for which the Fredholm properties of their elements are available , In particular, some bounds for indices of the mentioned operators ar e found. This fact includes a (weak) necessary condition for the inver tibility. (C) 1998 Elsevier Science B.V.