论文标题
传输反应方程的弱伽勒金有限元法
The Weak Galerkin Finite Element Method for the Transport-Reaction Equation
论文作者
论文摘要
我们介绍并分析了一种薄弱的Galerkin有限元方法，用于求解$ d $空间维度的传输反应方程。通过允许在由任意多边形/polyhedra组成的一般网格上使用不连续的有限元，该方法是高度灵活的。我们得出了\ textColor [rgb] {0.00,0.00,1.00} {$ o o（h^{k+\ frac {1} {2}} {2}}} $ k $ k $ t th-th-th-th-th-fore th-th-forder tore to $ k的$ k \ geq 0 $ geq 0。此外，对于特殊的网格类别，我们还获得了\ textColor [rgb] {0.00,0.00,1.00} {最佳错误}估计$ O（H^{k+1}）$ - $ l_2 $ -norm中的订单。提出了一个衍生恢复公式，以近似对流\ textColor [rgb] {1.00,0.00,0.00} {方向导数}，并给出了相应的SuperConvergence估算。提供了有关兼容和非兼容网格的数值示例，以显示这种弱的Galerkin方法的有效性。
We present and analyze a weak Galerkin finite element method for solving the transport-reaction equation in $d$ space dimensions. This method is highly flexible by allowing the use of discontinuous finite element on general meshes consisting of arbitrary polygon/polyhedra. We derive the \textcolor[rgb]{0.00,0.00,1.00}{$L_2$-error estimate} of $O(h^{k+\frac{1}{2}})$-order for the discrete solution when the $k$th-order polynomials are used for $k\geq 0$. Moreover, for a special class of meshes, we also obtain the \textcolor[rgb]{0.00,0.00,1.00}{optimal error} estimate of $O(h^{k+1})$-order in the $L_2$-norm. A derivative recovery formula is presented to approximate the convection \textcolor[rgb]{1.00,0.00,0.00}{directional derivative} and the corresponding superconvergence estimate is given. Numerical examples on compatible and non-compatible meshes are provided to show the effectiveness of this weak Galerkin method.
