Title

A curl-conforming weak Galerkin method for the quad-curl problem

Document Type

Article

Publication Date

7-4-2019

Department

Department of Mathematical Sciences

Abstract

The quad-curl problem arises from the inverse electromagnetic scattering theory and magnetohydrodynamics. In this paper, a weak Galerkin method is proposed using the curl-conforming Nédélec elements. On one hand, the method avoids the construction of the curl–curl conforming elements and thus solves a smaller linear system. On the other hand, it is much simpler than the case of using the fully discontinuous elements. For polynomial spaces of order k, error estimates of O(hk−1) in the energy norm and of O(hk) in the H(curl) norm are established, which are validated by the numerical examples.

Publisher's Statement

© Springer Nature B.V. 2019. Publisher’s version of record: https://doi.org/10.1007/s10543-019-00764-5

Publication Title

BIT Numerical Mathematics

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