Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations

A parametric finite element method for fourth order geometric evolution equations

We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has v...

Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations

There are three important steps in the computational modelling of any physical process: (i) problem definition, (ii) mathematical model, and (iii) computer simulation. The first natural step is to define an idealization of our problem of interest in terms of a set of relevant quantities which we would like to measure. In defining this idealization we expect to obtain a well-posed problem, this ...

Multilevel Preconditioning for Finite Volume Element Methods

We consider precondition of linear systems resulting from the finite volume element method (FVEM) for elliptic boundary value problems. With the help of the interpolation operator from a trial space to a test space and the operator induced by the FVEM bilinear form, we show that both wavelet preconditioners and multilevel preconditioners designed originally for the finite element method for the...

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...