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Convergence estimates for multigrid algorithms without regularity assumptions. (English) Zbl 0727.65101

A new method for proving rate of convergence estimates of multigrid algorithms for symmetric positive definite problems is given. In contrast to the standard multigrid theory requiring a “regularity and approximation” assumption, the new theory requires only an easily verified approximation assumption. Numerical results are included.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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