SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 829-863, January 2021.
We consider a finite element method for elliptic equations with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. We assume minimal regularity of the solutions. A space decomposition as in FETI and BDCC induces an embarrassingly parallel preprocessing and leads to a final system of size independent of the coefficients. The resulting solution is in equilibrium, and all PDEs involved are elliptic. One of the problems in the pre-processing step is nonlocal but with exponentially decaying solutions, enabling a practical scheme where the basis functions have an extended, but still local, support. To make the method robust with respect to high-contrast coefficients, we enrich the space solution via local eigenvalue problems, obtaining an optimal a priori error estimate that mitigates the effect of having coefficients with different magnitudes. The technique developed is dimensional independent and easy to extend to other elliptic problems such as elasticity.

中文翻译：

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多尺度问题的混合局部谱分解

SIAM数值分析学报，第59卷，第2期，第829-863页，2021年1月。
我们考虑基于原始混合公式的具有非均质且可能具有高对比度系数的椭圆方程的有限元方法。我们假设解决方案的规律性最小。如FETI和BDCC中的空间分解会引起尴尬的并行预处理，并导致最终系统的大小独立于系数。所得溶液处于平衡状态，并且所有涉及的PDE均为椭圆形。预处理步骤中的问题之一是非局部的，但解决方案呈指数衰减，这使得基本方案具有扩展但仍是局部支持的实用方案成为可能。为了使该方法对高对比度系数具有鲁棒性，我们通过局部特征值问题丰富了空间解，获得最佳的先验误差估计，以减轻具有不同幅度系数的影响。开发的技术是尺寸无关的，并且易于扩展到其他椭圆形问题，例如弹性。