TY - GEN
T1 - Mixed plane wave discontinuous galerkin methods
AU - Hiptmair, Ralf
AU - Perugia, Ilaria
PY - 2009
Y1 - 2009
N2 - In this paper, we extend the class of plane wave discontinuous Galerkin methods for the two-dimensional inhomogeneous Helmholtz equation presented in Gittelson, Hiptmair, and Perugia [2007]. More precisely, we consider the case of numerical fluxes defined in mixed form, namely, numerical fluxes explicitly defined in terms of both the primal and the flux variable, instead of the primal variable and its gradient. In our error analysis, we rely heavily on the approximation results and inverse estimates for plane waves proved in Gittelson, Hiptmair, and Perugia [2007] and develop a new mixed duality argument.
AB - In this paper, we extend the class of plane wave discontinuous Galerkin methods for the two-dimensional inhomogeneous Helmholtz equation presented in Gittelson, Hiptmair, and Perugia [2007]. More precisely, we consider the case of numerical fluxes defined in mixed form, namely, numerical fluxes explicitly defined in terms of both the primal and the flux variable, instead of the primal variable and its gradient. In our error analysis, we rely heavily on the approximation results and inverse estimates for plane waves proved in Gittelson, Hiptmair, and Perugia [2007] and develop a new mixed duality argument.
UR - http://www.scopus.com/inward/record.url?scp=78651551240&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02677-5_5
DO - 10.1007/978-3-642-02677-5_5
M3 - Contribution to proceedings
AN - SCOPUS:78651551240
SN - 9783642026768
VL - 70 LNCSE
T3 - Lecture Notes in Computational Science and Engineering
SP - 51
EP - 62
BT - Domain Decomposition Methods in Science and Engineering XVIII
T2 - 18th International Conference of Domain Decomposition Methods
Y2 - 12 January 2008 through 17 January 2008
ER -