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A lower bound on the convergence rate of a two-level method with pointwise smoother for problems in H(curl).
Ludmil Zikatanov
Email: ludmil@psu.edu
Postal = 218 McAllister bldg, Department of Mathematics, Penn State, University Park, PA 16801
In this work, we prove a bound below on the convergence of the two-level method with a point-wise smoother for problem in H(curl). This result justifies a conclusion (usually based on numerical observations) that a point smoother does not lead to optimal multigrid method. In fact, we show that any smoother, that is equivalent to the diagonal of the stiffness matrix will result in a non-optimal method.