Summary
We consider two multiphysics problems in geomechanics with constraints. The first involves coupled solid deformation–fluid diffusion subject to a volume constraint in the limit of no-flow. The second is the classic contact problem subject to a no-interprenetration constraint. Both problems are known to generate unphysical oscillation in the pressure field when some combinations of displacement and pressure finite element interpolations are employed. We trace the problem to the non-satisfaction of the LBB condition and utilize a stabilization technique based on polynomial pressure projection to circumvent the unpreferable pressure oscillation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bochev, P.B., Dohrmann, C.R., Gunzburger, M.D.: Stabilization of low-order mixed finite elements for the stokes equations. SIAM J. Numer. Anal. 44, 82–101 (2006)
Brezzi, F.: A discourse on the stability conditions for mixed finite element formulations. Comput. Methods Appl. Mech. Eng. 82, 27–57 (1990)
Liu, F., Borja, R.I.: Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput. Methods Appl. Mech. Eng. 82, 27–57 (2010)
White, J.A., Borja, R.I.: Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. Comput. Methods Appl. Mech. Eng. 199, 2456–2471 (2008)
White, J.A.: Stabilized finite element methods for coupled flow and geomechanics. Ph.D. Thesis, Stanford University (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borja, R.I., White, J.A., Liu, F. (2011). CIRCUMVENTING THE VOLUME AND CONTACT CONSTRAINTS IN MULTIPHYSICS FINITE ELEMENT SIMULATIONS. In: Borja, R.I. (eds) Multiscale and Multiphysics Processes in Geomechanics. Springer Series in Geomechanics and Geoengineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19630-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-19630-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19629-4
Online ISBN: 978-3-642-19630-0
eBook Packages: EngineeringEngineering (R0)