Error analysis of a decoupled finite element method for quad-curl problems
Numerical Analysis
2021-12-09 v2 Numerical Analysis
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, an a posterior error estimator is developed and a separate marking adaptive finite element procedure is proposed, together with its convergence proved. Both the a priori and a posteriori error analysis are supported by the numerical examples.
Cite
@article{arxiv.2102.03396,
title = {Error analysis of a decoupled finite element method for quad-curl problems},
author = {Shuhao Cao and Long Chen and Xuehai Huang},
journal= {arXiv preprint arXiv:2102.03396},
year = {2021}
}