抛物方程一种新混合有限元格式及误差分析

摘要

研究二维抛物方程,提出一些新的、Brezzi-Babu(s)ka条件自然满足的混合变分格式、关于时间半离散混合格式和全离散化混合有限元格式,并对这些格式做严格误差分析.这种混合有限元格式不但自由度是最少的而且所得到的误差估计也是最优阶的,是对现有格式的改进和发展.%In this paper, two-dimensional parabolic equations are studied with mixed method.rnA type of new mixed variational formulations, time-semi-discrete mixed equations, and fullyrndiscrete mixed finite element formulations are derived, where Brezzi-Babuska's condition isrnautomatically satisfied. And some rigorous error analyses are provided. The degrees of freedomrnare not only minimum for these mixed finite element formulations, but their error estimatesrnalso optimal order. Moreover, it is shown that the methods here are the improvements andrnrenovations for existing all methods.