多孔介质流的BDF2有限元解的误差分析  

Optimal error estimates of a BDF2-FE scheme of porous media flow

作　　者：李瑜 张卓玥 蔡文涛 LI Yu;ZHANG Zhuoyue;CAI Wentao(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第4期50-56,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：浙江省自然科学基金资助项目(LY22A010019)。

摘　　要：提出多孔介质流方程的一种全离散有限元格式。在时间上采用2阶向后差分(Backward Differentiation Formula,BDF)有限元数值格式BDF2方法离散,空间上采用Galerkin-Galerkin有限元方法离散。由于非线性耦合项的存在,使得压力的有限元解的低阶精度“污染”了浓度的有限元解的误差估计,引入一个拟椭圆投影“切断”压力有限元解和浓度有限元解的联系。对浓度项和压力项采用同阶的有限元空间进行离散,进一步分析得到关于浓度和压力的有限元解的无条件最优L^(∞)(0,T;L^(2))误差估计。In this paper,a fully discrete finite element scheme is provided for the porous media flow,where BDF2 and Galerkin-Galerkin finite scheme are used in temporal direction and in spatial direction,respectively.In previous analysis method,due to the presence of nonlinear coupling term,the low-order accuracy of the finite element solution of pressure will“pollutes”the error estimate of the finite element solution of concentration,so that the error estimation of concentration is not optimal.Therefore,in this method,the concentration term and the pressure term are discretized by the same order finite element space,and we introduce a quasi-elliptic projection.This projection“cuts off”the connection between the finite element solution of pressure and the finite element solution of concentration.By further analysis,the unconditional optimal error estimate of the finite element solution of concentration can be obtained.

关 键 词：不可压缩多孔介质流 BDF2 有限元方法 最优误差估计 

分 类 号：O24[理学—计算数学]