Mixed schemes for quad-curl equations. (English) Zbl 1395.65147
Summary: In this paper, mixed schemes are presented for two variants of quad-curl equations. Specifically, stable equivalent mixed formulations for the model problems are presented, which can be discretized by finite elements of low regularity and of low degree. The regularities of the mixed formulations and thus equivalently the primal formulations are established, and some finite elements examples are given which can exploit the regularity of the solutions to an optimal extent.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 76E25 | Stability and instability of magnetohydrodynamic and electrohydrodynamic flows |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 35Q35 | PDEs in connection with fluid mechanics |
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