论文标题
$ l^p $ - 一阶传输问题的主要双二元元素方法
An $L^p$-primal-dual finite element method for first-order transport problems
论文作者
论文摘要
针对一阶运输问题提出了一种新的$ l^p $ - 主要二重弱级彩色方法（$ l^p $ -pdwg）。建立了$ l^p $ -pdwg数值解决方案的存在和独特性。此外，$ l^p $ -PDWG方法提供了一个数值解决方案，该解决方案在每个元素上保留本地保存。为原始变量建立了最佳订单误差估计。提出了一系列数值结果，以验证所提出的$ l^p $ -PDWG方案的效率和准确性。
A new $L^p$-primal-dual weak Galerkin method ($L^p$-PDWG) with $p>1$ is proposed for the first-order transport problems. The existence and uniqueness of the $L^p$-PDWG numerical solutions is established. In addition, the $L^p$-PDWG method offers a numerical solution which retains mass conservation locally on each element. An optimal order error estimate is established for the primal variable. A series of numerical results are presented to verify the efficiency and accuracy of the proposed $L^p$-PDWG scheme.
