Solution Techniques for Poroelasticity that Preserve Linear and Angular Momentum
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We propose a solution procedure for mixed formulations of elasticity that is capable of weakly preserving angular momentum and the symmetry of the stress based on [1, 2]. In this technique, we construct a particular solution that is consequently updated with a homogeneous correction. In this way, we rewrite the system from a saddle point problem to a series of symmetric positive definite systems that can be solved up to a desired accuracy. This allows us to iteratively create stress fields that preserve linear and angular momentum element-wise, while the error is concentrated in Hooke’s law. Extensions to the quasi-static Biot system are presented afterward and the talk is concluded with numerical experiments emphasizing the efficiency of the approach.
