Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
Congreve, Scott and Houston, Paul and Wihler, Thomas P. (2011) Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proceedings in Applied Mathematics and Mechanics, 11 (1). pp. 3-6. ISSN 1617-7061
In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented.
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