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The weak Galerkin finite element method for the transport-reaction equation
Journal of Computational Physics ( IF 3.8 ) Pub Date : 2020-03-12 , DOI: 10.1016/j.jcp.2020.109399
Tie Zhang , Shangyou Zhang

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 L2-error estimate of O(hk+12)-order for the discrete solution when the kth-order polynomials are used for k0. Moreover, for a special class of meshes, we also obtain the optimal error estimate of O(hk+1)-order in the L2-norm. A derivative recovery formula is presented to approximate the convection 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.



中文翻译:

输运反应方程的弱Galerkin有限元方法

我们提出并分析了弱Galerkin有限元方法来求解d空间维中的输运反应方程。通过允许在由任意多边形/多面体组成的普通网格上使用不连续有限元,此方法具有很高的灵活性。我们得出大号2的误差估计 ØHķ+1个2当使用k阶多项式来求解离散解时ķ0。此外,对于一类特殊的网格,我们还获得了ØHķ+1个中的顺序 大号2-规范。给出了一个导数恢复公式来近似对流方向导数,并给出了相应的超收敛估计。提供了有关兼容和不兼容网格的数值示例,以显示此弱Galerkin方法的有效性。

更新日期:2020-03-12
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