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Journal of Scientific Computing

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14-06-2018

Preconditioning of a Hybridized Discontinuous Galerkin Finite Element Method for the Stokes Equations

Authors: Sander Rhebergen, Garth N. Wells

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom that can be eliminated locally (cell-wise), thereby significantly reducing the size of the global problem. Although the linear system becomes more complex to analyze after static condensation of these element degrees-of-freedom, the pressure Schur complement of the original and reduced problem are the same. Using this fact, we prove spectral equivalence of this Schur complement to two simple matrices, which is then used to formulate optimal preconditioners for the statically condensed problem. Numerical simulations in two and three spatial dimensions demonstrate the good performance of the proposed preconditioners.

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Title: Preconditioning of a Hybridized Discontinuous Galerkin Finite Element Method for the Stokes Equations
Authors: Sander Rhebergen
Garth N. Wells
Publication date: 14-06-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0760-4

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