论文标题
进一步的抛物线PDE的时空FOSL公式
Further results on a space-time FOSLS formulation of parabolic PDEs
论文作者
论文摘要
在[2019年，抛物线方程的时空最小二乘有限元素，Arxiv：1911.01942]，由Führer＆Karkulik撰写，证明了时空一阶系统最小二乘形式的热量方程式。在目前的工作中，该结果被推广到具有可能不可分解的边界条件的一般二阶抛物线PDE，并证明了由最小二乘估计量驱动的标准自适应有限元方法的普通收敛。后者的证明很容易扩展到一大群最小二乘的配方。
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated. The proof of the latter easily extends to a large class of least-squares formulations.
