Published

A priori and a posteriori error analysis of a decoupled finite element method for quad-curl problems

Shuhao Cao, Long Chen, and Xuehai Huang

Journal of Scientific Computing, 90(1), 1-25, 2022

arXiv   bibtex

ABSTRACT:

 Finite element approximation to a decoupled formulation for
the quad--curl problem is studied in this paper. The difficulty of
constructing elements with certain conformity to the quad--curl
problems has been greatly reduced. For convex domains, where the
regularity assumption holds for Stokes equation, the approximation to
the curl of the true solution has quadratic order of convergence and
first order for the energy norm. If the solution shows singularity, a
posterior error estimator is developed and a separate marking adaptive
finite element procedure is proposed, together with its convergence
proved. Both a priori and a posteriori error analysis are supported by
the numerical examples.