Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
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DOI：
10.1137/11083143x
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
L. Jiang;D. Copeland;J. Moulton
中科院分区：
文献类型：
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作者：
L. Jiang;D. Copeland;J. Moulton
我们发展了一类求解二阶椭圆型方程的扩展混合多尺度有限元方法(MsFEM)及其杂交方法。该格式扩展了标准混合多尺度有限元格式，同时求解了四个未知量(混合格式)：压力、压力梯度、速度和拉格朗日乘子。我们使用多尺度基函数来表示压力的速度和梯度。在扩展的混合有限元框架中，我们同时考虑了可分离和不可分离的空间尺度。具体地说，我们分析了三类方法：周期可分尺度、G-收敛可分尺度和尺度连续体。在没有尺度分离的情况下，利用一些全局信息可以显著提高扩展混合MsFEM的精度。我们给出了这些方法的严格的收敛分析，包括协调和非协调公式。文中给出了各种多尺度模式的数值结果。
We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity, and Lagrange multipliers. We use multiscale basis functions for both the velocity and the gradient of pressure. In the expanded mixed MsFEM framework, we consider both separable and nonseparable spatial scales. Specifically, we analyze the methods in three categories: periodic separable scales, G-convergent separable scales, and a continuum of scales. When there is no scale separation, using some global information can significantly improve the accuracy of the expanded mixed MsFEMs. We present a rigorous convergence analysis of these methods that includes both conforming and nonconforming formulations. Numerical results are presented for various multiscale models o...