Titlebook: Symmetric Discontinuous Galerkin Methods for 1-D Waves; Fourier Analysis, Pr Aurora Marica,Enrique Zuazua Book 2014 Aurora Marica, Enrique

乞讨

misshapen

Aurora Marica,Enrique ZuazuaIncludes supplementary material:

联想记忆

HACK

Discontinuous Galerkin Approximations and Main Results,cular, we introduce the . (DG) semi-discretization of the . and . equations using the so-called symmetric interior penalty DG method in its simplest version, in which . are used on .. We then emphasize the main difficulties encountered when analyzing the observability inequality for the DG schemes,

痛苦一生

巩固

Fourier Analysis of the Discontinuous Galerkin Methods,mulas for the two classes of eigenvalues and eigenvectors of the Fourier symbol of the discrete Laplacian, the so-called . and . modes. In the last part of this chapter, we analyze fine properties of both Fourier modes as, for example, the behavior of the corresponding . which are first-order deriva

abduction

On the Lack of Uniform Observability for Discontinuous Galerkin Approximations of Waves,wave packets propagate arbitrarily slowly. Our construction is based on the fact that on each Fourier mode there are critical wave numbers at which the corresponding group velocity vanishes. Moreover, we prove that the observability constant blows up at least polynomially at any order as the mesh si

装入胶囊

Filtering Mechanisms,the classical . method or on the . filtering algorithm. We rigorously prove their efficiency to recover the uniform observability estimates as the mesh size parameter goes to zero. In the last section of this chapter, we present several numerical simulations showing in particular how solutions corre

canonical

暗指

2191-8198 lerkin (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 com