论文标题
反应扩散方程的超授权插值HDG方法II：HHO启发的方法
Superconvergent Interpolatory HDG methods for reaction diffusion equations II: HHO-inspired methods
论文作者
论文摘要
在J. Sci。 Comput。，81：2188-2212，2019，我们考虑了针对标量反应扩散方程式定义的超融合杂交不连续的盖尔金（HDG）方法（HDG）方法，并显示了如何定义插入式插入版本，从而维持其收敛性。插插方法使用本地后处理的近似解决方案来评估非线性项，并在时间间隔之前一次组装所有HDG矩阵，从而导致计算成本降低。结果方法显示了多项式度$ k \ ge 1 $的解决方案的超授权率。在这项工作中，我们利用了HDG和Hybrid高级（HHO）方法之间在Esaim Math中发现的链接。模型。 numer。肛门，50：635-650，2016，并将此想法扩展到新的HHO启发的HDG方法，该方法在由一般多面体元素制成的网格中定义，在其中发现了}。我们证明，所得的插值HDG方法以与线性椭圆问题相同的速率收敛。因此，我们通过某些方法获得了$ k \ ge 0 $的超授权方法。我们提出数值结果来说明收敛理论。
In J. Sci. Comput., 81: 2188-2212, 2019, we considered a superconvergent hybridizable discontinuous Galerkin (HDG) method, defined on simplicial meshes, for scalar reaction diffusion equations and showed how to define an interpolatory version which maintained its convergence properties. The interpolatory approach uses a locally postprocessed approximate solution to evaluate the nonlinear term, and assembles all HDG matrices once before the time intergration leading to a reduction in computational cost. The resulting method displays a superconvergent rate for the solution for polynomial degree $k\ge 1$. In this work, we take advantage of the link found between the HDG and the hybrid high-order (HHO) methods, in ESAIM Math. Model. Numer. Anal., 50: 635-650, 2016 and extend this idea to the new, HHO-inspired HDG methods, defined on meshes made of general polyhedral elements, uncovered therein}. We prove that the resulting interpolatory HDG methods converge at the same rate as for the linear elliptic problems. Hence, we obtain superconvergent methods for $k\ge 0$ by some methods. We present numerical results to illustrate the convergence theory.
