TY - JOUR
T1 - A space-time discontinuous galerkin method for the incompressible navier-stokes equations
AU - Rhebergen, Sander
AU - Cockburn, Bernardo
AU - van der Vegt, Jaap J.W.
PY - 2013
Y1 - 2013
N2 - We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily highorder accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method's robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.
AB - We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily highorder accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method's robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.
KW - Deforming domains
KW - Incompressible navier-stokes equations
KW - Space-time discontinuous galerkin method
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U2 - 10.1016/j.jcp.2012.08.052
DO - 10.1016/j.jcp.2012.08.052
M3 - Article
AN - SCOPUS:84870493532
SN - 0021-9991
VL - 233
SP - 339
EP - 358
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 1
ER -