Duality estimates for the numerical solution of integral equations
By a small modification of the statement and the proof of the Aubin- Nitsche lemma for Galerkin methods [cf. \textit{P. G. Ciarlet}, The finite element method for elliptic problems (1978; Zbl 0383.65058)] the authors arrive at duality estimates for the error of general projective methods. The estimates are applied to Galerkin methods as to boundary integral equations on plane domains with corners and and three-dimensional screen and crack problems, and to the collocation method as to the integral equation of the second kind with the double layer potential on a piecewise smooth curve. In the latter case, the integral equation is solved by nodal collocation using piecewise linear trial functions. In some cases the authors get higher order estimates where previous formulations of the duality arguments were not applicable. The estimates are confirmed by numerical results.
scientific article; zbMATH DE number 4084961
scientific article