拟线性抛物问题的非协调H^1-Galerkin扩展混合有限元方法

A Nonconforming H^1-Galerkin Expanded Mixed Finite Element Method for Semilinear Parabolic Partial Differential Equations

抛物方程在热的传导、溶质的弥散以及多孔介质的渗流等问题中有着广泛的应用.本文综合H1-Galerkin混合有限元方法与扩展混合有限元方法的优点,针对一类拟线性抛物问题,提出了在半离散和向后的Euler全离散格式下非协调的H1-Galerkin扩展混合有限元方法.该方法利用真解的插值,不需要利用投影,从而得到有限元解的存在唯一性和格式的稳定性,以及和以往协调元相同的误差估计.

The parabolic partial differential equations have wide range of applications in the heat transmission, the solute dissemination, porous media seepage and so on. In this paper, the nonconforming Galerkin expanded finite element method for a class of quasi-linear partial dif- ferential equations is proposed both for semi-discrete and back-ward Euler full discrete schemes by applying the advantages of Galerkin mixed finite element method and expanded finite ele- ment method. The same error estimates as the conforming case in the previous literature, the existence and uniqueness of the finite element solutions and the stability of the schemes are obtained by means of the interpolation of the true solutions instead of projections.