A new stabilizer free weak Galerkin (WG) method is introduced and analyzed for the biharmonic equation. Stabilizing/penalty terms are often necessary in the finite element formulations with discontinuous approximations to ensure the stability of the methods. Removal of stabilizers will simplify finite element formulations and reduce programming complexity. This stabilizer free WG method has an ultra simple formulation and can work on general partitions with polygons/polyhedra. Optimal order error estimates in a discrete $H^2$ for $k\ge 2$ and in $L^2$ norm for $k>2$ are established for the corresponding weak Galerkin finite element solutions. Numerical results are provided to confirm the theories.

中文翻译：

---

多面网格上双调和方程的一种无稳定器弱伽辽金方法

介绍了一种新的无稳定剂弱伽辽金（WG）方法并分析了双调和方程。在具有不连续近似的有限元公式中，稳定/惩罚项通常是必要的，以确保方法的稳定性。去除稳定器将简化有限元公式并降低编程复杂性。这种不含稳定剂的 WG 方法具有超简单的公式，可以处理具有多边形/多面体的一般分区。为相应的弱伽辽金有限元解建立了离散$H^2$ 中$k\ge 2$ 和$L^2$ 范数中$k>2$ 的最优阶误差估计。提供了数值结果来证实这些理论。