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2019 | OriginalPaper | Chapter

Mixed Formulation of a Linearized Lubrication Fracture Model in a Poro-elastic Medium

Authors : Vivette Girault, Mary F. Wheeler, Kundan Kumar, Gurpreet Singh

Published in: Contributions to Partial Differential Equations and Applications

Publisher: Springer International Publishing

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Abstract

We analyse and discretize a mixed formulation for a linearized lubrication fracture model in a poro-elastic medium. The displacement of the medium is expressed in primary variables while the flows in the medium and fracture are written in mixed form, with an additional unknown for the pressure in the fracture. The fracture is treated as a non-planar surface or curve according to the dimension, and the lubrication equation for the flow in the fracture is linearized. The resulting equations are discretized by finite elements adapted to primal variables for the displacement and mixed variables for the flow. Stability and a priori error estimates are derived. A fixed-stress algorithm is proposed for decoupling the computation of the displacement and flow and a numerical experiment is included.

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Title: Mixed Formulation of a Linearized Lubrication Fracture Model in a Poro-elastic Medium
Authors: Vivette Girault
Mary F. Wheeler
Kundan Kumar
Gurpreet Singh
Publisher: Springer International Publishing
Book: Contributions to Partial Differential Equations and Applications
Print ISBN: 978-3-319-78324-6

Electronic ISBN: 978-3-319-78325-3

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-78325-3_12

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