Volume 51, Number 4, July-August 2017
|Page(s)||1173 - 1195|
|Published online||21 June 2017|
Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order
1 Institute of Applied Mathematics (LS III), TU Dortmund, Vogelpothsweg 8, 44227 Dortmund, Germany.
2 Applied Mathematics III, Dept. of Mathematics, Cauerstr. 11, 91058 Erlangen, Germany.
Received: 22 September 2015
Revised: 17 June 2016
Accepted: 24 August 2016
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.
Mathematics Subject Classification: 65M12 / 65M60
Key words: Finite element method / time discretization / discontinuous Galerkin / preconditioning
© EDP Sciences, SMAI 2017
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