Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration

Congreve, Scott; Houston, Paul

Abstract

In this paper we propose a class of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem based on the application of a single step of a nonlinear Newton solver. We present both the a priori and a posteriori error analysis of this two-grid hp-version DGFEM as well as performing numerical experiments to validate the bounds.

Citation

Congreve, S., & Houston, P. Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration. Presented at Proceedings of the Eighth International Conference on Scientific Computing and Applications

• Conference Name: Proceedings of the Eighth International Conference on Scientific Computing and Applications
• End Date: Apr 4, 2012
• Publication Date: Jan 1, 2013
• Deposit Date: Aug 26, 2015
• Publicly Available Date: Aug 26, 2015
• Peer Reviewed: Peer Reviewed
• Keywords: discontinuous Galerkin methods, two-grid finite element methods
• Public URL: https://nottingham-repository.worktribe.com/output/1003747
• Additional Information: Published in: Recent advances in scientific computing and applications: Eighth International Conference on Scientific Computing and Applications, April 1-4, 2012, University of Nevada, Las Vegas, Nevada / Jichun Li, Hongtao Yang, Eric Machorro, editors. Providence, Rhode Island: American Mathematical Society, 2013. ISBN 9780821887370. doi: 10.1090/conm/586/11629