中文摘要：

提出了抛物型微分方程的高效多尺度数值计算方法.与传统有限元基函数相比,多尺度有限元基函数能更好地反映问题自身的强振荡微观信息,结合多尺度有限元格式,可使计算结果在宏观尺度获得很好的数值逼近.对时间采用欧拉向后差分离散化,得到稳定且收敛的数值结果.新方法在取得高仿真逼近的同时,节约了大量计算资源和时间,因而更具应用价值.

英文摘要：

An efficient multiscale finite element computation is proposed to solve the time-space parabolic problems.By comparing the standard finite element basis functions with the multiscale basis functions,the latter has the ability to reflect the local oscillating information,and by the multiscale finite element scheme it may achieve good approximation on the macroscopical scale.For time scale to apply the Euler backward difference discretization,the author demonstrates the stability and convergence by the numerical experiment.This new method obtains the good simulation,and at the same time it saves plenty of computer resource and time,as a consequence it is available for further application values.