Abstract
The application of a non-overlapping domain decomposition method to the solution of a stabilized finite element method for elliptic boundary value problems is considered. We derive an a-posteriori error estimate which bounds the error on the subdomains by the interface error of the subdomain solutions. As a by-product, some foundation is given to the design of the interface transmission condition. Numerical results support the theoretical results. Furthermore, we adapt a recent result on a-posteriori estimates for singular perturbation problems in order to obtain an a-posteriori estimate for the discrete subdomain solutions.
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Received April 28, 1999; revised November 1, 1999
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Lube, G., Müller, L. & Otto, F. A Non-Overlapping Domain Decomposition Method for the Advection-Diffusion Problem. Computing 64, 49–68 (2000). https://doi.org/10.1007/s006070050003
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DOI: https://doi.org/10.1007/s006070050003