论文标题
具有点奇点的声波的时空不连续的盖金近似
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities
论文作者
论文摘要
我们为多边形域中的线性，第二阶波方程$ω\ subset \ mathbb {r}^2 $开发了时空离散的收敛理论，这可能是由具有不同繁殖速度的分段同质介质所占据的。 Building on an unconditionally stable space-time DG formulation developed in [Moiola, Perugia 2018], we (a) prove optimal convergence rates for the space-time scheme with local isotropic corner mesh refinement on the spatial domain, and (b) demonstrate numerically optimal convergence rates of a suitable \emph{sparse} space-time version of the DG scheme.后一个方案基于所谓的\ emph {组合公式}，并结合一个各向异性时空DG-差异化。它导致最佳订单收敛方案，也是在具有角落的域中，具有多种自由度，它基本上像最优质的空间网格上$ω$的一个固定椭圆问题的DG解决方案一样。平滑和单数解的数值实验都支持整个和稀疏时空DG方案的空间精制网格的收敛率最佳性。
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $Ω\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds. Building on an unconditionally stable space-time DG formulation developed in [Moiola, Perugia 2018], we (a) prove optimal convergence rates for the space-time scheme with local isotropic corner mesh refinement on the spatial domain, and (b) demonstrate numerically optimal convergence rates of a suitable \emph{sparse} space-time version of the DG scheme. The latter scheme is based on the so-called \emph{combination formula}, in conjunction with a family of anisotropic space-time DG-discretizations. It results in optimal-order convergent schemes, also in domains with corners, with a number of degrees of freedom that scales essentially like the DG solution of one stationary elliptic problem in $Ω$ on the finest spatial grid. Numerical experiments for both smooth and singular solutions support convergence rate optimality on spatially refined meshes of the full and sparse space-time DG schemes.
