Twogrid hpversion discontinuous Galerkin finite element methods for secondorder quasilinear elliptic PDEsTools Congreve, Scott and Houston, Paul and Wihler, Thomas P. Twogrid hpversion discontinuous Galerkin finite element methods for secondorder quasilinear elliptic PDEs. Journal of Scientific Computing . ISSN 08857474 (Submitted)
Official URL: http://www.springer.com/mathematics/computational+science+%26+engineering/journal/10915
AbstractIn this article we propose a class of socalled twogrid hpversion discontinuous Galerkin finite element methods for the numerical solution of a secondorder 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 twogrid hpversion discontinuous Galerkin finite element method is developed. Moreover, we propose and implement an hpadaptive twogrid 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 threedimensional 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 twogrid approach is exploited, when compared to the standard discontinuous Galerkin method.
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