Course Description: This course provides a practical introduction to the Finite Element Method (FEM), with an emphasis on hands-on implementation using Python. It covers the basic theoretical concepts ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Finite Element Methods for solving problems with material and geometric nonlinearities; transient dynamics analysis with explicit and implicit time integration, partitioned methods, and stability; ...

Professor of Mechanics, Washington University, St. Louis, Mo. It's easy to construct finite-element models with errors. And it's just as easy to correct them, when you know how. The first step in a ...