An interior penalty method for a two dimensional curl-curl and grad-div problem

Susanne C Brenner, Li-yeng Sung, Jintao Cui


We study an interior penalty method for a two dimensional curl-curl and grad-div problem that appears in electromagnetics and in fluid-structure interactions. The method uses discontinuous $P_1$~vector fields on graded meshes and satisfies optimal convergence rates (up to an arbitrarily small parameter) in both the energy norm and the $L_2$~norm. These theoretical results are corroborated by results of numerical experiments.

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