Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration
Congreve, Scott and Houston, Paul (2013) Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration. In: Proceedings of the Eighth International Conference on Scientific Computing and Applications, 1-4 April 2012, Las Vegas, USA.
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.
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