Abstract

In this paper, we investigate the multigrid methods for the linear finite element approximation of elliptic problems with large jumps in coefficients. Some singular functions, which cause the deterioration of the convergence rate, are introduced in our space splitting. According to the space splitting, we construct a modified multigrid method and prove that its uniform convergence is independent of the mesh size and the jumps. As a result, we also prove that the conjugate gradient method with the ‘V’-cycle multigrid preconditioner converges uniformly.

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