ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Free access article

DOI: 10.1051/m2an:2000162
M2AN, Vol. 34, N $^{\rm o}$ 3, 2000, pp. 687-706

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

Zhiming Chen
Institute of Mathematics, Academia Sinica, Beijing 100080, P.R. China. (zmchen@math03.math.ac.cn)

Qiang Du
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. (madu@uxmail.ust.hk)

Received: March 16, 1999. Revised: September 14, 1999.

Abstract: 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.

Keywords and phrases: Mean field model, superconductivity, vortices, mixed finite element, unstructured grid, convergence analysis.

AMS Subject Classification: 65N99, 82D55

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