===affil2: Louisiana State University ===firstname: Duk-Soon ===firstname4: ===firstname3: ===lastname2: Brenner ===lastname: Oh ===firstname5: ===affil6: ===lastname3: ===email: duksoon@cct.lsu.edu ===lastname6: ===affil5: ===otherauths: ===lastname4: ===affil4: ===lastname7: ===affil7: ===firstname7: ===postal: 216 Johnston Hall Baton Rouge, LA 70803 ===firstname6: ===ABSTRACT: A multigrid method for vector field problems discretized with Raviart-Thomas finite elements is developed and analyzed. The smoother is based on a modified nonoverlapping domain decomposition methods and provides the uniform convergence of W-cycle algorithms. Numerical experiments that support the theory are also presented. This is joint work with Susanne Brenner. ===affil3: ===lastname5: ===affilother: ===title: A Smoother Based on Nonoverlapping Domain Decomposition Methods for H(div) problems ===firstname2: Susanne C.