We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical time-marching schemes) as well as locally in space-time refined meshes.

中文翻译：

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抛物线问题的插值算子

我们引入了具有近似和稳定性属性的插值算子，适用于原始和混合公式中的抛物线问题。我们得出张量乘积网格的局部误差估计（出现在经典时间推进方案中）以及时空细化网格中的局部误差估计。