变分多尺度有限元方法中分析/数值求解细尺度解的研究

ON THE FINE SCALES SOLVED ANALYTICALLY/NUMERICALLY IN THE VARIATIONAL MULTISCALE FINITE ELEMENT METHOD

变分多尺度有限元方法中的细尺度解对数值解有着重要的影响,其可通过分析方法或数值方法求得.作者在文中分别采用上述两种方法对细尺度解进行了求解,并将这两种求解方法用于对流占优的对流扩散方程的求解,比较了它们的优缺点.数值求解结果表明:求解对流占优的对流扩散方程时,虽然分析和数值求解细尺度的变分多尺度有限元法均能得到精确的数值解,但是后者比前者具有更高的稳定性,同时也需要较多的计算时间.

The fine scales solution in the variational rn＇ultiscale finite element method, which can be acquired by analytical or numerical technique, has an important impact on the final numerical solution. Therefore, the processes for obtaining fine scales solution by theSe two techniques are described, respectively. Meanwhile, they are applied to solve the advectiondiffusion equation, and their advantages and disadvantages are also compared. Numerical results indicate that the variational multiscale finite element method in which fine scales in derived numerically has better stability than that in which fine scales in derived analytically, although both can acquire accurate solutions.