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**1 - 1**of**1**### Convergence of Multigrid Algorithms Incorporating an Artificial Damping

"... When the solution and coefficients in a problem are highly oscillatory, there exists sometimes a glaring difference between solution and physical results. This occurrence can be arisen by the fact that the coarse grid problem is still huge and poorly-conditioned. In this case, one way for solving su ..."

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When the solution and coefficients in a problem are highly oscillatory, there exists sometimes a glaring difference between solution and physical results. This occurrence can be arisen by the fact that the coarse grid problem is still huge and poorly-conditioned. In this case, one way for solving such problems is to apply an artificial damping in multigrid algorithm. In [9], a multigrid algorithm incorporating an artificial damping has been used for solving a model problem, but the convergence proof has not been presented. In this paper, a multigrid algorithm is presented and the convergence of the algorithm is proved for a general problem.