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Higher order space-time elements for a non-linear Biot model

Borregales Reveron, Manuel Antonio; Radu, Florin Adrian
Conference object, Peer reviewed, Book
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URI
https://hdl.handle.net/1956/22586
Date
2019
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  • Department of Mathematics [637]
Original version
Borregales M., Radu F.A. (2019) Higher Order Space-Time Elements for a Non-linear Biot Model. In: Radu F., Kumar K., Berre I., Nordbotten J., Pop I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham   https://doi.org/10.1007/978-3-319-96415-7_49
Abstract
In this work, we consider a non-linear extension of the linear, quasi-static Biot’s model. Precisely, we assume that the volumetric strain and the fluid compressibility are non-linear functions. We propose a fully discrete numerical scheme for this model based on higher order space-time elements. We use mixed finite elements for the flow equation, (continuous) Galerkin finite elements for the mechanics and discontinuous Galerkin for the time discretization. We further use the L-scheme for linearising the system appearing on each time step. The stability of this approach is illustrated by a numerical experiment.
Publisher
Springer
Series
Lecture Notes in Computational Science and Engineering ; 126
Copyright
Copyright Springer Nature Switzerland AG 2019

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