This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization for the space. Due to the low regularity of the data of the problem, the solution possesses very low regularity in the entire domain. A priori error bound in the $L^2(L^2(\Omega))$-norm for the spatially discrete finite element approximations are derived under minimal regularity with the help of the $L^2$ projection operators and the duality argument. The interfaces are assumed to be smooth for our purpose.

翻译：本文章研究了线性抛物线接口的先验误差分析,即测量数据在紧凑的 convex多边形域中的时间问题,用$\mathb{R ⁇ 2$。我们使用了标准的连续安装的有限元素分解空间标准。由于问题数据的规律性较低,解决方案在整个域中具有非常低的规律性。 由$L2(L2)(2/L2)(\Omega))中约束的空间离散元素近似的先验误差,在最小的常规下,在$L2$的投影操作员和双元参数的帮助下,在最小的常规下得出。我们假定这些界面为我们的目的是顺畅的。