拋物問題的伽遼金有限元方法 25(第2版)（簡體書）

In the mid 1960s, a number of papers appeared independently in the numerical analysis literature which were con-cerned with the construction and analysis of finite difference schemes for elliptic problems by variational principles, e.g., Céa [45], Demjanovic [68],Feng [98], Friedrichs and Keller [101], and Oganesjan and Ruchovets [187].By considering approximating functions as defined at all points rather than at meshpoints, the mathematical theory of finite elements then became es-tablished through contributions such as Birkhoff, Schultz and Varga [27],where the theory of splines was brought to bear on the development, and Zlámal [250], with the first stringent error analysis of more complicated el-ements. The duality argument for the L2 error estimate quoted in Theorem 1.1 was developed independently by Aubin [7], Nitsche [179] and Oganesjan and Ruchovets [188], and later maximum-norm error estimates such as (1.44) were shown by Scott [214], Natterer [175], and Nitsche [182], see Schatz and Wahlbin [208]. The sharpness of this estimate, with the logarithmic factor,was shown in Haverkamp [116].
General treatments of the mathematics of the finite element method for elliptic problems can be found in textbooks such as, e.g., Babuska and Aziz [11], Strang and Fix [221], Ciarlet [51] and Brenner and Scott [42], and we shall sometimes quote these for background material.
The development of the theory of finite elements for parabolic problems started around 1970. At this time finite difference analysis for such problems had reached a high level of refinement after the fundamental 1928 paper by Courant, Friedrichs and Lewy [52], and became the background and starting point for the finite element analysis of such problems.