The work is concerned with two problems: (a) analysis of a discontinuous Petrov–Galerkin (DPG) method set up in fractional energy spaces, (b) use of the results to investigate a non-conforming version of the DPG method for general polyhedral meshes. We use the ultraweak variational formulation for the model Laplace equation. The theoretical estimates are supported with 3D numerical experiments.

中文翻译：

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基于分数Sobolev范数的多面体网格非合格DPG方法分析

这项工作涉及两个问题：（a）分析在分数能量空间中建立的不连续Petrov-Galerkin（DPG）方法，（b）使用结果研究一般多面体的DPG方法的不合格版本网格。我们对模型Laplace方程使用超弱变分公式。理论估计得到3D数值实验的支持。