论文标题
非散发形式椭圆形偏微分方程的计算多尺度方法
Computational multiscale methods for nondivergence-form elliptic partial differential equations
论文作者
论文摘要
本文提出了新的计算多尺度方法，用于非胶合形式的线性二阶偏微分方程，并具有满足绳索条件的异质系数。该结构遵循局部正交分解（LOD）的方法，并通过以数值同质化的精神以细微的规模解决局部细胞问题，提供了操作员适应的粗空间。粗空间的自由度与均质问题的不合格和混合有限元方法有关。一种示例性方法的严格误差分析表明，从发散形式PDES已知的LOD方法的有利属性，即，其适用性和准确性超出了规模分离和周期性，对于非佛罗内格形式的问题仍然有效。
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the methodology of localized orthogonal decomposition (LOD) and provides operator-adapted coarse spaces by solving localized cell problems on a fine scale in the spirit of numerical homogenization. The degrees of freedom of the coarse spaces are related to nonconforming and mixed finite element methods for homogeneous problems. The rigorous error analysis of one exemplary approach shows that the favorable properties of the LOD methodology known from divergence-form PDEs, i.e., its applicability and accuracy beyond scale separation and periodicity, remain valid for problems in nondivergence-form.
