一反应扩散模型解的有限元方法和误差分析

１引言在地下水运移过程中，污染物（溶质）随地下水在含水层中运移，并常常发生各种化学反应．文献［１－３］等提出并论述了三种化学物质（如Ｍ１，Ｍ２和Ｍ３）之间发生的一类化学反应．文献［４，５］等建立和描述了这类反应的数学模型（Ｐ）．文献［６，７」的作者首次对模型（Ｐ）进行了理论上的定性分析，主要是利用上，下解方法，算子半群理论和Ｓｏｂｏｌｅｖ空间的般人定理等论证了模型（Ｐ）的整体古典解的存在唯一性和渐近性质，文［６，７］也讨论了整体解的极限性态和收敛性估计．此外，文［８，９］等也就模型（Ｐ）的一类特…

FINITE ELEMENT METHODS AND ERROR ANALYSIS FOR A REACTION-DIFFUSION MODEL

The paper is concerned with a mathematical for some chemical reaction which take place in ground water. The model can be decribed by the following initial boundary value problem (P) of the semilinear reaction-diffusion system: Where RN is a bounded domain, the boundary are is properly smooth, J= (0, T], di>0(i=1, 2, 3) are constants. i,j,m,r are positive integers, u,v,w are unkown functions, are given initial functions. Galerkin approximating scheme of (P) is deduced by making use of the finite element method. Besides, the analysis of the conveyance for the approximating solution and the optimal error estimates in L2 are demonstrated by taking advantage of the priori estimate theory and technique of differential equation.