论文标题
Biharmonic方程的无稳定器$ c^0 $弱的Galerkin方法
A stabilizer-free $C^0$ weak Galerkin method for the biharmonic equations
论文作者
论文摘要
在本文中，我们介绍并分析了无稳定器的$ C^0 $弱Galerkin（SF-C0WG）方法，用于解决Biharmonic问题。 SF-C0WG方法是根据$ C^0 $ C^0 $连续的分段$ K+2 $的分段多项式制定的，$ k+2 $，$ k \ geq 0 $以及面部未知数是不连续的$ k+1 $的不连续的分段多项式。这种SF-C0WG方法的表述没有稳定或罚款项，并且与Biharmonic问题的$ C^1 $符合有限元方案一样简单。离散的$ H^2 $ stard中的最佳订单错误估计值和$ h^1 $ norm for $ k \ geq 0 $是针对相应的WG有限元解决方案建立的。 $ l^2 $ norm中的错误估算也将以$ k> 0 $的最佳收敛顺序得出，而$ k = 0 $的互惠顺序也是如此。证明了数值实验以确认理论结果。
In this article, we present and analyze a stabilizer-free $C^0$ weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is formulated in terms of cell unknowns which are $C^0$ continuous piecewise polynomials of degree $k+2$ with $k\geq 0$ and in terms of face unknowns which are discontinuous piecewise polynomials of degree $k+1$. The formulation of this SF-C0WG method is without the stabilized or penalty term and is as simple as the $C^1$ conforming finite element scheme of the biharmonic problem. Optimal order error estimates in a discrete $H^2$-like norm and the $H^1$ norm for $k\geq 0$ are established for the corresponding WG finite element solutions. Error estimates in the $L^2$ norm are also derived with an optimal order of convergence for $k>0$ and sub-optimal order of convergence for $k=0$. Numerical experiments are shown to confirm the theoretical results.
