论文标题
多项式还原的新的弱梯度，用于稳定器弱绒毛法。
A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction
论文作者
论文摘要
弱伽勒金（WG）有限元方法是一种用于求解部分微分方程的有效且灵活的一般数值技术。它是不连续近似的经典符合有限元方法的自然扩展，该方法保持简单的有限元公式。稳定器游离弱彩色方法进一步简化了WG方法并降低了计算复杂性。本文探讨了多项式空间最佳组合的可能性，从而最大程度地减少了稳定器无WG方案中未知数的数量，而不会损害数值近似的准确性。提出了一种新的稳定剂弱绿素有限元法，并通过多项式降低进行分析。为了实现这样的目标，引入了弱梯度的新定义。在离散的$ H^1 $ NORM和标准$ L^2 $ Norm中，为相应的WG近似值建立了最佳顺序的错误估计。在各种网格上测试了数值示例，并确认该理论。
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous approximations, which maintains simple finite element formulation. Stabilizer free weak Galerkin methods further simplify the WG methods and reduce computational complexity. This paper explores the possibility of optimal combination of polynomial spaces that minimize the number of unknowns in the stabilizer free WG schemes without compromising the accuracy of the numerical approximation. A new stabilizer free weak Galerkin finite element method is proposed and analyzed with polynomial degree reduction. To achieve such a goal, a new definition of weak gradient is introduced. Error estimates of optimal order are established for the corresponding WG approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. The numerical examples are tested on various meshes and confirm the theory.
