@article{697340,
      recid = {697340},
      author = {Marica, Aurora, and Zuazua, E.},
      title = {Symmetric discontinuous Galerkin approximations of 1-D  waves Fourier analysis, propagation, observability and  applications / [electronic resource] :},
      pages = {1 online resource.},
      abstract = {This workdescribes the propagation properties of the  so-called symmetric interior penalty discontinuous Galerkin  (SIPG) approximations of the 1-d wave equation. This is  done by means of linear approximations on uniform meshes.  First,a careful Fourier analysis is constructed,  highlightingthe coexistence of two Fourier spectral  branches or spectral diagrams (physical and spurious)  related to the two components of the numerical solution  (averages and jumps). Efficient filtering mechanisms are  also developedby means of techniques previously proved to  be appropriate for classical schemes like finite  differences or P1-classical finite elements. In  particular,the work presents a proof thatthe uniform  observability property is recovered uniformly by  considering initial data with null jumps and averages given  by a bi-grid filtering algorithm. Finally, the bookexplains  how theseresults can be extended to other more  sophisticated conforming and non-conforming finite element  methods, in particular to quadratic finiteelements, local  discontinuous Galerkin methods and a version of the SIPG  method adding penalization on the normal derivatives of the  numerical solution at the grid points. This work is the  first publication tocontaina rigorous analysis of the  discontinuous Galerkin methods for wave control problems.  It will be of interest to a range of researchers  specializing inwave approximations.},
      url = {http://library.usi.edu/record/697340},
      doi = {https://doi.org/10.1007/978-1-4614-5811-1},
}