Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Fully discrete finite element approaches for time-dependent Maxwell's equations

Many problems in sciences and industry involve the solutions of Maxwell’s equations, for example, problems arising in plasma physics, microwave devices, diffraction of electromagnetic waves. In this paper, we are interested in the numerical solution of time-dependent Maxwell’s equations in a bounded polyhedral domain in three dimensions. In the literature, one can find a great deal of work on n...

Analysis of Fully Discrete Finite Element Methods for a System of Differential Equations Modeling Swelling Dynamics of Polymer Gels

The primary goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is governed by the solvent permeation and the elastic interaction; the permeation is described by a pressure equation for the solvent, and the elastic int...

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

Finite element methods for Maxwell's equations

Adaptive finite element methods for Maxwell equations

We report our recent efforts in developing adaptive finite element methods for solving electromagnetic problems. We shall first introduce the method for the Maxwell cavity problem with discontinuous coefficients. We then consider the eddy current model with voltage excitations for complicated three dimensional structures. Unique continuation on analytic curve and its application to Inverse Prob...