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...

We derive explicit formulas for the eigenvalues and eigenvectors of the Discrete Laplacian on a rectangular grid for the standard finite difference and finite element methods in 1D, 2D, and 3D. Periodic, Dirichlet, Neumann, and mixed boundary conditions are all considered. We show how the higher dimensional operators can be written as sums of tensor products of one dimensional operators, and th...

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved an...

The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in H(div) and the velocity in L2. Any standard mixed finite element function space can be utilized for this mixed formulation, e.g., the Raviart-Thomas discretization which is r...

explosion has always been regarded as one of the most complicated engineering problems. as a result, many engineers have preferred rather simplified empirical approaches in comparison to extremely complex deterministic analyses. in this paper, however, a numerical simulation based on the combined finite/discrete element methodology is presented for analyzing the dynamic behavior of fracturing r...

In [Z. Cai, C. Tong, P. S. Vassilevski, and C. Wang, Numer. Methods Partial Differential Equations, to appear], the authors developed and analyzed a mixed finite element method for the stationary Stokes equations based on the pseudostress-velocity formulation. The pseudostress and the velocity are approximated by a stable pair of finite elements: Raviart–Thomas elements of index k ≥ 0 and disco...