论文标题
面向目标的各向异性$ HP $ - 适应不连续的Galerkin方法
Goal-oriented anisotropic $hp$-adaptive discontinuous Galerkin method for the Euler equations
论文作者
论文摘要
我们借助不连续的盖尔金（DG）方法来处理可压缩欧拉方程的数值解，重点是面向目标的误差估计和适应性。我们分析了DG方案的伴随一致性，其中双重问题不是通过DG形式和目标功能的分化来提出的，而是使用非线性形式的合适的线性化。此外，我们介绍了欧拉方程的面向目标的各向异性$ hp $ -MENS-MENS适应技术。理论结果由数值实验支持。
We deal with the numerical solution of the compressible Euler equations with the aid of the discontinuous Galerkin (DG) method with focus on the goal-oriented error estimates and adaptivity. We analyze the adjoint consistency of the DG scheme where the dual problem is not formulated by the differentiation of the DG form and the target functional but using a suitable linearization of the nonlinear forms. Further, we present the goal-oriented anisotropic $hp$-mesh adaptation technique for the Euler equations. The theoretical results are supported by numerical experiments.
