期刊
APPLIED NUMERICAL MATHEMATICS
卷 83, 期 -, 页码 51-71出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2014.04.011
关键词
Continuous Galerkin-Petrov method; Discontinuous Galerkin method; Incompressible Navier-Stokes equations; Newton-multigrid solver
资金
- German Research Association (DFG) [SCHI 576/2-1, TU 102/35-1]
- Higher Education Commission (HEC) of Pakistan [LC06052]
In this paper, we discuss solution techniques of Newton-multigrid type for the resulting nonlinear saddle-point block-systems if higher order continuous Galerkin-Petrov (cGP(k)) and discontinuous Galerkin (dG(k)) time discretizations are applied to the nonstationary incompressible Navier-Stokes equations. In particular for the cGP(2) method with quadratic ansatz functions in time, which lead to 3rd order accuracy in the L-2-norm and even to 4th order superconvergence in the endpoints of the time intervals, together with the finite element pair Q(2)/P-1(disc) for the spatial approximation of velocity and pressure leading to a globally 3rd order scheme, we explain the algorithmic details as well as implementation aspects. All presented solvers are analyzed with respect to their numerical costs for two prototypical flow configurations. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
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