This study focuses on a reduced-order extrapolation method for the coefficient vectors of the mixed finite element solution for two-dimensional fourth-order hyperbolic equation. We first establish the mixed finite element scheme for the equation and give the matrix model of the mixed finite element scheme and the existence, stability and error estimates of its solutions. Then, we derive a reduced-order extrapolation mixed finite element matrix model with a small number of unknowns, where the proper orthogonal decomposition method is used to save central processing unit time, and prove the existence, stability and error estimates of the reduced-order extrapolation mixed finite element solutions with the help of matrix knowledge. More importantly, the reduced-order extrapolation mixed finite element matrix model have the same basis functions and error accuracy as the mixed finite element matrix model. Finally, some numerical experiments confirm the effectiveness of the reduced-order extrapolation mixed finite element matrix model, where the central processing unit time is greatly reduced and the accuracy is maintained.

We consider a mass conservative type method for semiconductor device problem by employing mixed finite element method (FEM) for electric potential equation and mass conservative characteristic FEM for both electron and hole density equations. The boundedness of numerical solution without certain time‐step restriction and optimal error estimates of full discrete scheme are proved. Numerical experiment is presented to verify the effectiveness and unconditional stability of the proposed method.

Herein, we discuss a mixed finite element method applied to the Brinkman equation of fluid motion in porous medium, which covers a field of situation from the Darcy equation to the Stokes problem associated with various perturbation parameters. The finite element based on staggered meshes is shown to be stable and effective with each case as the corresponding error estimates for both velocity and pressure are established. Finally, we present numerical examples confirming the theoretical analysis and the stability of the finite spaces approximation.