论文标题
弱彩素有限元方法中的弯曲元素
Curved Elements in Weak Galerkin Finite Element Methods
论文作者
论文摘要
当在有限元分区的内部涉及弯曲元件或/和整个域的边界上，在二维的内部边缘上涉及弯曲元件时，为泊松方程的弱伽勒金有限元方法建立了数学分析。在$ h^1 $ -NORM和$ l^2 $ -NORM中，弱Galerkin近似值的最佳错误估计值均已建立。据报道，数值结果证明了弱绿素方法在一般曲线多边形分区上的性能。
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on the boundary of the whole domain in two dimensions. The optimal orders of error estimates for the weak Galerkin approximations in both the $H^1$-norm and the $L^2$-norm are established. Numerical results are reported to demonstrate the performance of the weak Galerkin methods on general curved polygonal partitions.
