A dG Approach to Higher Order ALE Formulations in Time

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

doi:10.1007/978-3-319-01818-8_10

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2017

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“…[1,31,32] to name a few. Moreover variational time discretization schemes are particularly well suited to discretize problems on time-dependent domains, see [4,5]. However, Galerkin time discretization is not that popular among practitioners.…”

Section: Introductionmentioning

confidence: 99%

Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order

Basting¹,

Bänsch²

2017

ESAIM: M2AN

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We develop a preconditioner for systems arising from space-time finite element discretizations of parabolic equations. The preconditioner is based on a transformation of the coupled system into block diagonal form and an efficient solution strategy for the arising 2 × 2 blocks. The suggested strategy makes use of an inexact factorization of the Schur complement of these blocks, for which uniform bounds on the condition number can be proven. The main computational effort of the preconditioner lies in solving implicit Euler-like problems, which allows for the usage of efficient standard solvers. Numerical experiments are performed to corroborate our theoretical findings.

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