We propose new locking-free finite element methods for Biot’s consolidation model by coupling nonconforming and mixed finite elements. We show a priori error estimates of semidiscrete and fully discrete solutions. The main advantage of our method is that a uniform-in-time pressure error estimate is provided with an analytic proof. In our error analysis, we do not use Grönwall’s inequality, so t...

21  Abstract—This paper describes a numerical solution for plane elasticity problem. It includes algorithms for discretization by mixed finite element methods. The discrete scheme allows the utilization of Brezzi-Douglas-Fortin-Marini (BDFM2) for the stress tensor and piecewise linear elements for the displacement. The numerical results are compared with some previously published works or with...

In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular...