A mixed method for axisymmetric div-curl systems

Copeland, Dylan; Gopalakrishnan, Jayadeep; Pasciak, Joseph

doi:10.1090/S0025-5718-08-02102-9

A mixed method for axisymmetric div-curl systems
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by Dylan M. Copeland, Jayadeep Gopalakrishnan and Joseph E. Pasciak;

Math. Comp. 77 (2008), 1941-1965

DOI: https://doi.org/10.1090/S0025-5718-08-02102-9

Published electronically: March 10, 2008

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Abstract:

We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.

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