000			02411nam a22003255i 4500
001			65274
005			20210426134807.0
010			_a978-1-4614-5811-1 _dcompra
090			_a65274
100			_a20150401d2014 k||y0pory50 ba
101			_aeng
102			_aUS
200			_aSymmetric discontinuous Galerkin methods for 1-D waves _bDocumento electrónico _eFourier analysis, propagation, observability and applications _fAurora Marica, Enrique Zuazua
210			_aNew York, NY _cSpringer _d2014
215			_aXVI, 104 p. _cil.
225			_aSpringerBriefs in Mathematics
300			_aColocação: Online
303			_aThis 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.  This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.
606			_aOndas
606			_aMétodos de Galerkin
606			_aTeoria da aproximação
680			_aQC157
700			_aMarica _bAurora
701			_932352 _aZuazua _bEnrique _4070
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-1-4614-5811-1
942			_2lcc _cF _n0