DeepAI AI Chat
Log In Sign Up

Numerical solution of the div-curl problem by finite element exterior calculus

by   Pascal Azerad, et al.
Université de Montpellier

We are interested in the numerical reconstruction of a vector field with prescribed divergence and curl in a general domain of R 3 or R 2 , not necessarily contractible. To this aim, we introduce some basic concepts of finite element exterieur calculus and rely heavily on recent results of P. Leopardi and A. Stern. The goal of the paper is to take advantage of the links between usual vector calculus and exterior calculus and show the interest of the exterior calculus framework, without too much prior knowledge of the subject. We start by describing the method used for contractible domains and its implementation using the FEniCS library (see We then address the problems encountered with non contractible domains and general boundary conditions and explain how to adapt the method to handle these cases. Finally we give some numerical results obtained with this method, in dimension 2 and 3.


page 13

page 14


Local Finite Element Approximation of Sobolev Differential Forms

We address fundamental aspects in the approximation theory of vector-val...

A C^0 finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain

In this paper, we study the biharmonic equation with the Navier boundary...

An hp-hierarchical framework for the finite element exterior calculus

The problem of solving partial differential equations (PDEs) on manifold...

Parallelized Discrete Exterior Calculus for Three-Dimensional Elliptic Problems

A formulation of elliptic boundary value problems is used to develop the...

Reissner-Mindlin shell theory based on tangential differential calculus

The linear Reissner-Mindlin shell theory is reformulated in the frame of...

Symmetric bases for finite element exterior calculus spaces

In 2006, Arnold, Falk, and Winther developed finite element exterior cal...