We first give a general error estimate for the nonconforming approximation of a problem for which a Banach-Ne{\v c}as-Babu{\v s}ka (BNB) inequality holds. This framework covers parabolic problems with general conditions in time (initial value problems as well as periodic problems) under minimal regularity assumptions. We consider approximations by two types of space-time discretizations, both based on a conforming Galerkin method in space. The first one is the Euler $\theta$--scheme. In this case, we show that the BNB inequality is always satisfied, and may require an extra condition on the time step for $\theta$ $\le$ 1 2. The second one is the time discontinuous Galerkin method, where the BNB condition holds without any additional condition.
翻译：首先给出一个非协调逼近的一般误差估计，该问题满足Banach-Ne{\v c}as-Babu{\v s}ka (BNB)不等式。该框架包括在时间上具有一般条件的抛物问题(初始值问题以及周期问题)，在最小的正则性假设下。我们考虑两种空时离散化的逼近方法，均基于空间的协调Galerkin方法。第一种是欧拉$\theta$方案。在这种情况下，我们表明BNB不等式总是成立的，并且可能需要一个额外的时间步长条件$\theta$ $\le$ 1 2。第二个是时间间断的Galerkin方法，其中BNB条件不需要任何额外的条件。
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