One of the common classes of equations that is encountered in several branches of science is partial differential equations. So in this article, I look at a software package called FreeFem++ that is ...

Optimal control problems are mathematical formulations used to determine control strategies that yield a desired outcome while minimising a prescribed cost function. In many applications, these ...

The finite element method is a powerful numerical technique that is used in all major engineering industries - in this video we'll explore how it works. We'll look at why it's useful to split the body ...

The Helmholtz equation is a fundamental partial differential equation that underpins the analysis of wave propagation, acoustic scattering and electromagnetic phenomena. Its numerical solution is ...

SIAM Journal on Numerical Analysis, Vol. 35, No. 2 (Apr., 1998), pp. 560-571 (12 pages) A new mixed finite element method is formulated for the Stokes equations, in which the two components of the ...

Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 383-401 (19 pages) In this paper a new explicit finite element method for numerically solving the drift-diffusion semiconductor device ...