Three‐dimensional modeling of problems in poro‐elasticity via a mixed least‐squares method using linear tetrahedral elements |
| |
| Authors: | Maria Tchonkova John Peters Stein Sture |
| |
| Institution: | 1. 9009 Great Hills Trail, Suite 224, Austin, TX 78759, U.S.A.;2. US Army Engineer Research and Development Center, Vicksburg, MS 39190, U.S.A.;3. Department of Civil, Environmental and Architectural Engineering, Campus Box 428, University of Colorado at Boulder, Boulder, CO 80309, U.S.A. |
| |
| Abstract: | In a previous publication we developed a new mixed least‐squares method for poro‐elasticity. The approximate solution was obtained via a minimization of a least‐squares functional, based upon the equations of equilibrium, the equations of continuity and weak forms of the constitutive relationships for elasticity and Darcy flow. The formulation involved four independent types of variables: displacements, stresses, pore pressures and velocities. All of them were approximated by linear continuous triangles. Encouraged by the computational results, obtained from the two‐dimensional implementation of the method, we extended our formulation to three dimensions. In this paper we present numerical examples for the performance of continuous linear tetrahedra within the context of the mixed least‐squares method. The initial results suggest that the method works well in the nearly and entirely incompressible limits for elasticity. For poro‐elasticity, the obtained pore pressures are stable without exhibiting the oscillations, which are observed when the standard Galerkin formulation is used. Copyright © 2010 John Wiley & Sons, Ltd. |
| |
| Keywords: | poro‐elsticity Darcy flow mixed finite elements |
|
|
