The weak Galerkin form of the finite element method, requiring only C⁰ basis function, is applied to the biharmonic equation. The computational procedure is thoroughly considered. Local orthogonal bases on triangulations are constructed using various sets of interpolation points with the Gram-Schmidt or Levenberg-Marquardt methods. Comparison and high-precision computations are carried out, and convergence rates are provided up to degree 11 for L², 10 for H¹, and 9 for H², suggesting that the algorithm is useful for a variety of computations.

中文翻译：

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四阶问题的弱Galerkin方法的高精度计算

仅需要C ⁰基函数的有限元方法的弱Galerkin形式应用于双调和方程。仔细考虑了计算过程。使用Gram-Schmidt或Levenberg-Marquardt方法使用各种插值点集构造基于三角剖分的局部正交基。比较和高精度的计算被执行，并且设置收敛速率高达11度为大号²，10 ħ ¹和9为ħ ²，这表明，该算法是用于各种计算是有用的。