The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is introduced in the gWG scheme to allow arbitrary combinations of piecewise polynomial functions defined in the interior and on the boundary of general polygonal or polyhedral elements. The error estimates are established for the numerical approximation in a discrete H^2 norm and a L^2 norm. The numerical results are reported to demonstrate the accuracy and flexibility of our proposed gWG method for the biharmonic equation.
翻译:为双调方程提议并分析通用的弱加列尔金(gWG)有限元素方法,在GWG办法中引入一种新的普遍离散弱二级部分衍生物,允许任意组合在内部和一般多边形或多边形元素边界上界定的片断多元函数,为离散的H ⁇ 2规范的数值近似值和L ⁇ 2规范设定了误差估计数,报告的数字结果是为了表明我们提议的双调方程的GWG方法的准确性和灵活性。