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Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
2009 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 47, no 5, 3820-3848 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we developed and analyzed a new class of discontinuous Galerkin (DG) methods for the acoustic

wave equation in mixed form. Traditional mixed finite element (FE) methods produce energy conserving schemes, but these

schemes are implicit, making the time-stepping inefficient. Standard DG methods give explicit schemes, but these approaches

are typically dissipative or suboptimally convergent, depending on the choice of numerical fluxes. Our new method can be

seen as a compromise between these two kinds of techniques, in the way that it is both explicit and energy conserving, locally

and globally. Moreover, it can be seen as a generalized version of the Raviart-Thomas FE method and the finite volume

method. Stability and convergence of the new method are rigorously analyzed, and we have shown that the method is optimally

convergent. Furthermore, in order to apply the new method for unbounded domains, we proposed a new way to handle the

second order absorbing boundary condition. The stability of the resulting numerical scheme is analyzed.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2009. Vol. 47, no 5, 3820-3848 p.
Keyword [en]
discontinuous Galerkin, optimal convergence, acoustic wave, absorbing boundary condition, energy conservation, stability analysis
National Category
URN: urn:nbn:se:kth:diva-72261DOI: 10.1137/080729062ISI: 000277836000011OAI: diva2:487465
QC 20120207Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2012-02-07Bibliographically approved

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