Presenters-0666
From CSDMS
CSDMS 2025: Exploring Earth's Surface with Models, Data & AI
The finite element method (FEM)
Abstract
There are in essence three comprehensive frameworks to numerically approximate the solution of (i.e., "solve") partial differential equations: The finite difference method (FDM), the finite volume method (FVM), and the finite element method (FEM). There have been clinics about the FDM and FVM at past CSDMS Annual Meetings; this clinic will introduce the FEM. Specifically, I will (i) outline the philosophical idea behind the FEM, (ii) how that differs from the FDM and the FVM, (iii) how the FEM is described mathematically, and (iv) how this translates into implementations. For the FEM, there exist a number of large, widely used, well documented, and extensively tested open source libraries that have been used for essentially all partial differential equations one can think of. I will base this clinic on lectures I have been using to teach the FEM for the past 25 years, utilizing in part the open source library deal.II (https://www.dealii.org/) of which I am one of the principal authors.
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