Year: 2011
Type: preprint
Abstract: There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus. However, we are not aware of any numerical experiments where mixed finite elements derived from discretizations of exterior calculus are used for a surface domain. This short note shows results of our preliminary experiments using mixed methods for Darcy flow (hence scalar Poisson's equation in mixed form) on surfaces. We demonstrate two numerical methods. One is derived from the primal-dual Discrete Exterior Calculus and the other from lowest order finite element exterior calculus. The programming was done in the language Python, using the PyDEC package which makes the code very short and easy to read. The qualitative convergence studies seem to be promising.
Source: arXiv (Cornell University)
Authors: Hirani, Anil N., Kalyanaraman, Kaushik
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W1801739641