We identify a norm on the pressure variable in the Stokes equation that allows us to prove a continuous inf-sup condition with a constant independent of the domain's aspect ratio. This is in contrast to the standard inf-sup constant, which breaks down as the aspect ratio increases. We further apply our result to construct robust operator preconditioners for the Stokes problem in slender domains. Several numerical examples illustrate the theory.

翻译：我们为Stokes方程中的压力变量定义了一种范数，该范数使我们能够证明一个与域纵横比无关的连续inf-sup条件。这与标准的inf-sup常数形成对比，后者会随着纵横比增大而失效。我们进一步应用该结果，为细长域中的Stokes问题构建了鲁棒的算子预条件子。若干数值算例验证了理论的有效性。