论文标题
连续的$ hp- $网状型号，用于不连续的彼得 - 盖尔金有限元方案，具有最佳的测试功能
A Continuous $hp-$Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions
论文作者
论文摘要
我们使用连续的网格模型为不连续的Petrov-Galerkin（DPG）有限元元素方案提出了各向异性$ HP-$网状改编策略，并具有最佳的测试功能，从而扩展了我们以前的$ H- $适应性工作。提出的策略利用了DPG离散化的内置基于残余的误差估计器来计算网格元素的多项式分布和各向异性。为了预测近似的最佳顺序，我们解决了元素斑块上的局部问题，从而使这些计算高度可行。连续网格模型是针对解决方案中的误差而制定的，该误差以适当的规范测量，或者在某些可允许的目标功能方面进行了测量。我们使用三角网格上的几个数值示例证明了拟议策略的性能。 关键字：不连续的彼得罗夫 - 盖尔金，连续的网格型号，$ hp- $改编，各向异性
We present an anisotropic $hp-$mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work on $h-$adaptation. The proposed strategy utilizes the inbuilt residual-based error estimator of the DPG discretization to compute both the polynomial distribution and the anisotropy of the mesh elements. In order to predict the optimal order of approximation, we solve local problems on element patches, thus making these computations highly parallelizable. The continuous mesh model is formulated either with respect to the error in the solution, measured in a suitable norm, or with respect to certain admissible target functionals. We demonstrate the performance of the proposed strategy using several numerical examples on triangular grids. Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$ adaptations, Anisotropy
