Local error estimates for some Petrov-Galerkin methods applied to strongly elliptic equations on curves

Author:
Jukka Saranen

Journal:
Math. Comp. **48** (1987), 485-502

MSC:
Primary 65R20; Secondary 35S99, 45J05, 65L10, 65N35

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878686-9

MathSciNet review:
878686

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Abstract: In this article we derive local error estimates for some Petrov-Galerkin methods applied to strongly elliptic equations on smooth curves of the plane. The results, e.g., cover the basic first-kind and second-kind integral equations appearing in the boundary element solution of the potential problem. The discretization model includes the Galerkin method and the collocation method using smoothest splines as trial functions. Asymptotic error estimates are given for a large scale of the Sobolev norms.

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Article copyright:
© Copyright 1987
American Mathematical Society