This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption. In this manuscript, we explain the error analysis of Lagrange interpolation on (possibly anisotropic) tetrahedrons. This topic is hardly explained in standard textbooks of the mathematical theory of finite element methods. The authors hope that this manuscript will be merged into a new textbook in future. Therefore, this manuscript is not intended to be a research paper. Supposed readers are students and researchers who are familiar with the mathematical theory of the finite element methods.
翻译:本文是无需形状正则性假设的单纯形单元插值误差分析系列讲义的第二部分。本手稿阐述了(可能各向异性的)四面体上拉格朗日插值的误差分析。这一主题在有限元方法数学理论的标准教科书中鲜有涉及。作者期望本手稿未来能融入新编教材,因此本手稿并非研究论文。目标读者为熟悉有限元方法数学理论的学生及研究者。