A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Biot Consolidation Model (Journal of Computational Mathematics, 2024)
A mixed finite element method is presented for the Biot consolidation problem in poroelasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviartnonconforming finite elements, while the fluid pressure is approximated by using the nodeconforming finite elements. The well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is alsoderived. Numerical experiments are provided to validate the theoretical results.
Keywords: Poroelasticity; Nonconforming finite element; Inf-sup condition; A priori error estimate.