论文标题
内部惩罚不连续的盖尔金方法的双重分析，在最低规律性和对先验的应用和helmholtz问题的后验误差分析
Duality analysis of interior penalty discontinuous Galerkin methods under minimal regularity and application to the a priori and a posteriori error analysis of Helmholtz problems
论文作者
论文摘要
我们考虑了由Helmholtz方程建模的时谐波传播问题的内部惩罚不连续的Galerkin离散，并得出了小说的先验和后验估计。我们的分析通常依赖于Aubin-Nitsche类型的二元性参数，其独创性是它适用于最少的规律性假设。我们获得的估计值直接概括了符合离散化的已知结果，即离散解决方案在合适的能量规范中是最佳的，并且可以通过后验估计器明确控制误差，前提是网格足够好。
We consider interior penalty discontinuous Galerkin discretizations of time-harmonic wave propagation problems modeled by the Helmholtz equation, and derive novel a priori and a posteriori estimates. Our analysis classically relies on duality arguments of Aubin-Nitsche type, and its originality is that it applies under minimal regularity assumptions. The estimates we obtain directly generalize known results for conforming discretizations, namely that the discrete solution is optimal in a suitable energy norm and that the error can be explicitly controlled by a posteriori estimators, provided the mesh is sufficiently fine.
