Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
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
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.
discontinuous Galerkin, optimal convergence, acoustic wave, absorbing boundary condition, energy conservation, stability analysis
IdentifiersURN: urn:nbn:se:kth:diva-72261DOI: 10.1137/080729062ISI: 000277836000011OAI: oai:DiVA.org:kth-72261DiVA: diva2:487465
QC 201202072012-01-312012-01-312012-02-07Bibliographically approved