标题： 抛物方程的空间-时间最小二乘有限元 显示英文标题

标题： Space-time least-squares finite elements for parabolic equations

摘要： 我们提出一种用于热方程的时空最小二乘有限元方法。 它基于在时空中等价一阶系统的L2范数中残差最小化。 这意味着（i）得到的双线性形式是对称和强制的，因此任何符合离散化都是均匀稳定的，（ii）刚度矩阵是对称的、正定的和稀疏的，（iii）我们可以免费获得局部后验误差估计器。 特别是，我们的方法具有完整的时空自适应性。 我们还提出了在高度结构化的单纯形时空网格上的先验误差分析。 数值结果结束本工作。 显示英文摘要

摘要： We present a space-time least squares finite element method for the heat equation. It is based on residual minimization in L2 norms in space-time of an equivalent first order system. This implies that (i) the resulting bilinear form is symmetric and coercive and hence any conforming discretization is uniformly stable, (ii) stiffness matrices are symmetric, positive definite, and sparse, (iii) we have a local a-posteriori error estimator for free. In particular, our approach features full space-time adaptivity. We also present a-priori error analysis on simplicial space-time meshes which are highly structured. Numerical results conclude this work.