ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

An upwinding mixed finite element method for a mean field model of superconducting vortices

Chen, Zhiminga1 and Du, Qianga2

a1 Institute of Mathematics, Academia Sinica, Beijing 100080, P.R. China. e-mail:

a2 Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, and Department of Mathematics, Iowa State University, Ames, IA 50011, USA. e-mail:


In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.

(Received March 16 1999)

(Revised September 14 1999)

(Online publication April 15 2002)

Key Words:

  • Mean field model;
  • superconductivity;
  • vortices;
  • mixed finite element;
  • unstructured grid;
  • convergence analysis.

Mathematics Subject Classification:

  • 65N99;
  • 82D55