书目名称 | Symmetric Discontinuous Galerkin Methods for 1-D Waves |
副标题 | Fourier Analysis, Pr |
编辑 | Aurora Marica,Enrique Zuazua |
视频video | http://file.papertrans.cn/884/883876/883876.mp4 |
概述 | Includes supplementary material: |
丛书名称 | SpringerBriefs in Mathematics |
图书封面 |  |
描述 | This work describes 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, highlighting the 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 developed by 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 that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, 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. |
出版日期 | Book 2014 |
关键词 | discontinuous Galerkin approximation; linear approximation; non-uniform propagation properties; physica |
版次 | 1 |
doi | https://doi.org/10.1007/978-1-4614-5811-1 |
isbn_softcover | 978-1-4614-5810-4 |
isbn_ebook | 978-1-4614-5811-1Series ISSN 2191-8198 Series E-ISSN 2191-8201 |
issn_series | 2191-8198 |
copyright | Aurora Marica, Enrique Zuazua 2014 |