论文标题
自适应修饰的弱甘草有限元法的收敛性和最佳性
Convergence and optimality of an adaptive modified weak Galerkin finite element method
论文作者
论文摘要
除了其收敛性和最佳性外，还研究了本文的自适应修饰的弱彩色方法（AMWG），用于椭圆问题。在不需要骨骼变量的情况下，简化了修改的弱彩色双线性形式，并且近似空间被选择为不连续的多项式空间，就像不连续的galerkin方法一样。在可靠的基于残差的后验误差估计器中，提出了一种自适应算法及其收敛性和用于最低订单情况的准选项。主要工具是桥接修改的弱彩手方法与Crouzeix-Raviart不合格元素之间的连接。与具有不连续多项式近似空间的方法的传统收敛分析不同，AMWG的收敛性是无惩罚参数。提出数值结果以支持理论结果。
An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal variable, and the approximation space is chosen as the discontinuous polynomial space as in the discontinuous Galerkin method. Upon a reliable residual-based a posteriori error estimator, an adaptive algorithm is proposed together with its convergence and quasi-optimality proved for the lowest order case. The primary tool is to bridge the connection between the modified weak Galerkin method and the Crouzeix-Raviart nonconforming finite element. Unlike the traditional convergence analysis for methods with a discontinuous polynomial approximation space, the convergence of AmWG is penalty parameter free. Numerical results are presented to support the theoretical results.
