%0 Generic %1 bansal2020spacetime %A Bansal, Pratyuksh %A Moiola, Andrea %A Perugia, Ilaria %A Schwab, Christoph %D 2020 %K convergence spacetime %T Space-time discontinuous Galerkin approximation of acoustic waves with point singularities %U http://arxiv.org/abs/2002.11575 %X We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $Ømega\subsetR^2$, 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 sparse space-time version of the DG scheme. The latter scheme is based on the so-called 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 $Ømega$ 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.

@misc{bansal2020spacetime, abstract = {We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, 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 $\Omega$ 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.}, added-at = {2021-06-09T16:53:11.000+0200}, author = {Bansal, Pratyuksh and Moiola, Andrea and Perugia, Ilaria and Schwab, Christoph}, biburl = {https://www.bibsonomy.org/bibtex/2990efcf000ccb6c982884c351f052493/dagon}, description = {Space-time discontinuous Galerkin approximation of acoustic waves with point singularities - 2002.11575.pdf}, interhash = {94254d8935053303c7cdee318e14854d}, intrahash = {990efcf000ccb6c982884c351f052493}, keywords = {convergence spacetime}, note = {cite arxiv:2002.11575Comment: 38 pages, 8 figures}, timestamp = {2021-06-09T16:53:35.000+0200}, title = {Space-time discontinuous Galerkin approximation of acoustic waves with point singularities}, url = {http://arxiv.org/abs/2002.11575}, year = 2020 }