We describe a domain decomposition algorithm for use in the parallel adaptive meshing paradigm of Bank and Holst SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443; SIAM Rev., 45 (2003), pp. 291--323]. Our algorithm has low communication, makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. Numerical examples illustrate the effectiveness of the procedure.
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