Abstract
We consider a non-overlapping domain decomposition method for diffusion-reaction problems which is known to converge strongly from previous work. We derive an a posteriori estimate which bounds the errors on the subdomains by the difference of traces of the subdomain solutions. If the domain decomposition method is discretized by finite elements we can adapt the techniques of the usual a posteriori error analysis for finite elements to get an a posteriori estimate for the discrete subdomain solutions.
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