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An Iteratively Decoupled Algorithm with Unconditional Stability for Biot's Consolidation Model

Abstract: In this talk, I shall introduce an iterative solution of a decoupled algorithm for Biot's consolidation model. By introducing an intermediate variable, we come up with an iteratively decoupled algorithm based on the three-field reformulation. As spatial discretization, we apply the Taylor–Hood elements for mechanics and Lagrange finite elements for flow. Besides, the implicit Euler scheme is used for the time discretization. The iterative strategy allows the results of our decoupled scheme to approach the solutions of the coupled algorithm. Moreover, the approach is proved to be unconditionally convergent. Further, numerical results are presented to illustrate good performances of the iterative method.