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中文摘要：
本文研究了二维空间中光滑的凸区域上具有小周期参数的抛物型方程的半离散双尺度有限元逼近。在整个区域上,利用二次元解均匀化问题;在参考单胞内,利用线性元解辅助问题;然后,将求得的有限元解代入多尺度渐近展开式,得到原问题解的一个半离散双尺度有限元格式。利用多尺度渐近展开和有限元理论,证明了该格式的收敛性。
英文摘要：
We study the parabolic equation with small periodic coeffcients in a smooth convex do-main of two-dimensional space and derive a semi-discrete two-scale finite element approximation in the paper.In the whole domain,we solve the homogenization problem with a quadratic element.In the reference cell,we solve the auxiliary problem with a linear element.Using the obtained finite element solutions to replace the solutions in the multi-scale asymptotic expansion,we get a semi-discrete two-scale finite element scheme for the original problem.Using the multi-scale asymptotic expansion and the finite element theory,we prove that the new scheme is convergen.
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