A new mixed nite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity. This new mixed discretization ts the geometric shapes of the discontinuity of the rough coeecients and domain boundaries well. This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas's mixed ...

In this paper, we develop a class of mixed finite element methods for the ferrofluid flow model proposed by Shliomis (1972). We show that energy stability weak solutions to is preserved exactly both semi-discrete and fully discrete solutions. Furthermore, prove existence uniqueness derive optimal error estimates schemes. Numerical experiments confirm theoretical results.

We consider control-volume mixed finite element methods for the approximation of second-order elliptic problems on rectangular grids. These methods associate control volumes (covolumes) with the vector variable as well as the scalar, obtaining local algebraic representation of the vector equation (e.g., Darcy’s law) as well as the scalar equation (e.g., conservation of mass). We establish O(h2)...

Finite element methods in which two spaces are used to approximate two different variables receive the general denomination of mixed methods. In some cases, the second variable is introduced in the formulation of the problem because of its physical interest and it is usually related with some derivatives of the original variable. This is the case, for example, in the elasticity equations, where...

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed...

This paper studies a phase field model for the mixture of two immiscible and incompressible fluids. The model is described by a nonlinear parabolic system consisting of the nonstationary Stokes equations coupled with the Allen-Cahn equation through an extra phase induced stress term in the Stokes equations and a fluid induced transport term in the Allen-Cahn equation. Both semi-discrete and ful...

A new mixed finite element method is proposed and analyzed for simulating two-phase droplet motion in a micro-scale device driven by Electrowetting-On-Dielectric (EWOD). The new feature of the method is that the finite element scheme is based on a weak formulation of the problem which includes the position of the moving interface and the curvature of its boundary as basic unknowns to be determi...