Geodesic
Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order
Basting, Steffen1 ; Bänsch, Eberhard2 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1173-1195

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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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DOI : 10.1051/m2an/2016055
Classification : 65M12, 65M60
Keywords: Finite element method, time discretization, discontinuous Galerkin, preconditioning

Basting, Steffen 1 ; Bänsch, Eberhard 2

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. 
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     title = {Preconditioners for the {Discontinuous} {Galerkin} time-stepping method of arbitrary order},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1173--1195},
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Basting, Steffen; Bänsch, Eberhard. Preconditioners for the Discontinuous Galerkin time-stepping method of arbitrary order. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1173-1195. doi: 10.1051/m2an/2016055

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