## A coupling of nonconforming and mixed finite element methods for Biot’s consolidation model.(English)Zbl 1274.74455

Summary: We develop a nonconforming mixed finite element method to solve Biot’s consolidation model. In particular, this work has been motivated to overcome nonphysical oscillations in the pressure variable, which is known as locking in poroelasticity. The method is based on a coupling of a nonconforming finite element method for the displacement of the solid phase with a standard mixed finite element method for the pressure and velocity of the fluid phase. The discrete Korn’s inequality has been achieved by adding a jump term to the discrete variational formulation. We prove a rigorous proof of a-priori error estimates for both semidiscrete and fully-discrete schemes. Optimal error estimates have been derived. In particular, optimality in the pressure, measured in different norms, has been proved for both cases when the constrained specific storage coefficient $$c_{0}$$ is strictly positive and when $$c_{0}$$ is nonnegative. Numerical results illustrate the accuracy of the method and also show the effectiveness of the method to overcome the nonphysical pressure oscillations.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics
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### References:

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