A C 0 conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C 0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C 1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H 2 norm and the L 2 norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

中文翻译：

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三角形/四面体双调和方程的 AC 0 符合 dg 有限元方法

一种C 0引入符合不连续伽辽金（CDG）有限元法求解双调和方程。第一个强梯度C 0有限元函数是不连续分段多项式的向量。第二个梯度是不连续分段多项式的弱梯度。这种方法，顾名思义，使用不合格（非C 1) 近似并保持符合有限元方法的简单公式化，而无需任何稳定器。离散的最优阶误差估计H 2规范和大号 2为相应的有限元解建立范数。给出了数值结果来证实收敛理论。