A weak Galerkin mixed finite element method for second order elliptic problems
A weak Galerkin mixed finite element method for second order elliptic problems
复制标题
DOI：
10.1090/s0025-5718-2014-02852-4
复制
发表时间：
2012-02
期刊：
影响因子：
--
通讯作者：
Junping Wang;X. Ye
中科院分区：
文献类型：
--
作者：
Junping Wang;X. Ye
**摘要**：针对表述为两个一阶线性方程组成的系统的二阶椭圆方程，引入并分析了一种新的弱伽辽金（WG）方法。这种称为WG - MFEM的方法是通过在具有任意多边形/多面体形状的有限元剖分上使用不连续分段多项式来设计的。WG - MFEM能够为主要变量和通量变量提供非常精确的数值近似。允许在任意形状的多边形/多面体上使用不连续逼近函数使得该方法在实际计算中具有高度的灵活性。针对相应的弱伽辽金混合有限元解，在离散的H范数和L范数下都建立了最优阶误差估计。
Abstract. A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. Allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation. Optimal order error estimates in both discrete H and L norms are established for the corresponding weak Galerkin mixed finite element solutions.