Gradient recovery based finite element methods for the two-dimensional quad-curl problem

In this paper, we construct two novel gradient recovery based linear element methods for the quad-curl equation appears in two dimensions. Among all the existing finite elements solving the quad-curl equation, our approach is the simplest as the used finite elements only have 3 degrees of freedom(DOFs). Numerical experiments also demonstrate that our proposed methods have nice convergence property, that is, it has optimal convergence rates under L2 and H1 norms and has superconvergence phenomenons under the recovery derivative.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, two novel gradient recovery based linear element methods are proposed for solving the quad-curl equation in two dimensions. Compared to existing finite element methods, our approach is the simplest as it only utilizes finite elements with 3 degrees of freedom (DOFs). Numerical experiments show that our proposed methods have excellent convergence properties, with optimal convergence rates under L2 and H1 norms and superconvergence phenomena under the recovery derivative.