On a Sharp Estimate of Overlapping Schwarz Methods in H(curl;Ω) and H(div;Ω)

04/20/2023

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by   Qigang Liang, et al.

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The previous proved-bound is C(1+H^2/δ^2) for the condition number of the overlapping domain decomposition H(curl;Ω) and H(div;Ω) methods, where H and δ are the sizes of subdomains and overlaps respectively. But all numerical results indicate that the best bound is C(1+H/δ). In this work, we solve this long-standing open problem by proving that C(1+H/δ) is indeed the best bound.