@article { , title = {Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs}, abstract = {In this article 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 of monotone type. The key idea in this setting is to first discretise the underlying nonlinear problem on a coarse finite element space V\_\{H,P\}. The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearise the underlying discretisation on the finer space V\_\{h,p\}; thereby, only a linear system of equations is solved on the richer space V\_\{h,p\}. In this article both the a priori and a posteriori error analysis of the two-grid hp-version discontinuous Galerkin finite element method is developed. Moreover, we propose and implement an hp-adaptive two-grid algorithm, which is capable of designing both the coarse and fine finite element spaces V\_\{H,P\} and V\_\{h,p\}, respectively, in an automatic fashion. Numerical experiments are presented for both two- and three-dimensional problems; in each case, we demonstrate that the cpu time required to compute the numerical solution to a given accuracy is typically less when the two-grid approach is exploited, when compared to the standard discontinuous Galerkin method.}, eissn = {0885-7474}, issn = {0885-7474}, journal = {Journal of Scientific Computing}, publicationstatus = {Submitted}, publisher = {Springer Verlag}, url = {https://nottingham-repository.worktribe.com/output/1025989}, author = {Congreve, Scott and Houston, Paul and Wihler, Thomas P.} }