Abstract
We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a discontinuous variational time discretization. For the spatial discretization of the subproblem of flow mixed finite element techniques are applied. The spatial discretization of the subproblem of mechanical deformation uses discontinuous Galerkin methods. They have shown their ability to eliminate locking that sometimes arises in numerical algorithms for poroelasticity and causes nonphysical pressure oscillations.
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References
M. Bause, F. Radu, U. Köcher, Space-time finite element approximation of the Biot poroelasticity system with iterative coupling. Comput. Methods Appl. Mech. Eng. 320, 745–768 (2017)
J.W. Both, M. Borregales, J.M. Nordbotton, K. Kundan, F.A. Radu, Robust fixed stress splitting for Biot’s equations in heterogeneous media. Appl. Math. Lett. 68, 101–108 (2017)
A. Mikelić, M. Wheeler, Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17, 479–496 (2013)
P. Philips, M. Wheeler, A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity. Comput. Geosci. 12, 417–435 (2008)
P. Philips, M. Wheeler, Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach. Comput. Geosci. 13, 5–12 (2009)
S.-Y. Yi, A study of two modes of locking in poroelasticity. SIAM J. Numer. Anal. 55, 1915–1936 (2017)
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Bause, M. (2019). Iterative Coupling of Mixed and Discontinuous Galerkin Methods for Poroelasticity. 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_50
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DOI: https://doi.org/10.1007/978-3-319-96415-7_50
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