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

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Book 2014 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.

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Symmetric Discontinuous Galerkin Methods for 1-D WavesFourier Analysis, Pr

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Preliminaries,ous finite elements (..-FEM) that we will consider in the next chapters, we also present some well-known results stating the lack of uniform observability estimates for the FD and ..-FEM approximations of the wave equation and the efficiency of the corresponding filtering strategies based on the Fourier truncation and the bi-grid algorithm.

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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 size . tends to zero.

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978-1-4614-5810-4Aurora Marica, Enrique Zuazua 2014

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SpringerBriefs in Mathematicshttp://image.papertrans.cn/t/image/883876.jpg

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https://doi.org/10.1007/978-1-4614-5811-1discontinuous Galerkin approximation; linear approximation; non-uniform propagation properties; physica