Discontinuous finite element methods for a bi-wave equation modeling $d$-wave superconductors.

This paper concerns discontinuous finite element approximations of a fourth-order bi-wave equation arising as a simplified Ginzburg-Landau-type model for $ d$ $ \vert\mathrm{ln} h\vert$-norm are established for the proposed Morley-type nonconforming method. In the second half of the paper, we develop a symmetric interior penalty discontinuous Galerkin method for the bi-wave equation using general meshes and prove optimal order error estimates in the energy norm. Finally, numerical experiments are provided to gauge the efficiency of the proposed methods and to validate the theoretical error bounds. [ABSTRACT FROM AUTHOR]