We present locally stabilized, conforming space-time finite element methods for parabolic evolution equations on hexahedral decompositions of the space-time cylinder. Tensor-product decompositions allow for anisotropic a priori error estimates, that are explicit in spatial and temporal meshsizes. Moreover, tensor-product finite elements are suitable for anisotropic adaptive mesh refinement strategies provided that an appropriate a posteriori discretization error estimator is available. We present such anisotropic adaptive strategies together with numerical experiments.

翻译：我们提出当地稳定、符合空间时气瓶六分解的抛物线进化方程式空间-时间有限元素方法。Tensor产品分解允许对厌异性先验误差进行估计,这在空间和时空网格中是明确的。此外,对于厌异性适应性调整网格精细战略来说,有抗异性产品有限元素是合适的,条件是具备适当的后代离散错误估计器。我们提出了这种异异异性适应策略以及数字实验。