Finite element methods are based on the variational formulation of partial differential equations which only need to compute the gradient of a function. Although unknowns are still associated to nodes, the function composed by piece-wise polynomials on each element and thus the gradient can be computed element-wise. Finite element spaces can thus be constructed on general triangulations and thi...

My research focuses on applied aspects of the calculus of variations and partial differential equations, particularly nonlinear equations arising from physics and chemistry, and numerical analysis and scientific computing, particularly finite-element analysis and numerical methods for interface motion. I have worked on mathematical and numerical problems arising from materials science, such as ...

We describe the development and implementation of an eecient spectral element code for simulating transitional ows in complex three-dimensional domains. Critical to this eeort is the use of geometrically nonconforming elements that allow localized reenement in regions of interest, coupled with a stabilized high-order time-split formulation of the semi-discrete Navier-Stokes equations. Simulatio...

In this paper, various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed. Detailed descriptions of test/trial spaces, explicit and implicit formulations, nodal and edge/facet element basis functions are given, along with the numerical stability properties of the different methods. The advantages and disadvantages of mass lumping are ...