The affluent literature of finite element methods applied to linear parabolic problems, generally, produces numerical procedures with satisfactory properties from a numerical approximation point of view. However, some initial, boundary conditions or abrupt sink/source terms may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of tim...

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...

A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.