The Schwarz Algorithm for Spectral Methods
- 1 February 1988
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 25 (1) , 24-40
- https://doi.org/10.1137/0725003
Abstract
Recently, the Schwarz alternating method has been successfully coupled to spatial discretizations of spectral type, in order to solve boundary value, problems in complex, geometries with infinite order accuracy. In this paper, a simple version of the method is considered. A proof of its convergence is given in the energy norm, exploiting the properties of discrete-harmonic polynomials and a discrete maximum principle for spectral methods. More general situations can be handled theoretically in one space dimensionKeywords
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