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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 Poissons 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.
We derive a numerical method for Darcy flow, hence also for Poissons equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its d
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topo
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Dela
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the server-line pro
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a co