论文标题
一种加权混合杂交的不连续的盖尔金方法，用于漂移扩散问题
A weighted Hybridizable Discontinuous Galerkin method for drift-diffusion problems
论文作者
论文摘要
在这项工作中，我们提出了一种用于漂移扩散问题的可加权杂交不连续的Galerkin方法（W-HDG）。通过在离散化的每个单元格中计算$ l^2 $的乘积时，使用特定的指数权重，我们能够模仿Slotboom变量的行为，并从本地矩阵贡献中消除了漂移项，同时仍解决了primal变量的问题。我们表明，所提出的数值方案已得到充分验证，并在数值上验证它具有与经典HDG方法相同的属性，包括最佳收敛和后处理溶液的超授权。对于多项式程度零，尺寸一和消失的HDG稳定参数，W-HDG与Scharfetter-Gummel有限体积方案（即，它产生相同的系统矩阵）一致。局部指数权重的使用概括了Scharfetter-Gummel方案（用于运输主导问题的有限体积离散化的最先进）到任意高阶近似值。
In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the $L^2$ product in each cell of the discretization, we are able to mimic the behavior of the Slotboom variables, and eliminate the drift term from the local matrix contributions, while still solving the problem for the primal variables. We show that the proposed numerical scheme is well-posed, and validate numerically that it has the same properties as classical HDG methods, including optimal convergence, and superconvergence of postprocessed solutions. For polynomial degree zero, dimension one, and vanishing HDG stabilization parameter, W-HDG coincides with the Scharfetter-Gummel finite volume scheme (i.e., it produces the same system matrix). The use of local exponential weights generalizes the Scharfetter-Gummel scheme (the state-of-the-art for finite volume discretization of transport dominated problems) to arbitrary high order approximations.
