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Title: Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear PDEs
Author: Congreve, Scott
ISNI:       0000 0004 5353 8808
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2014
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In this thesis we study so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear partial differential equations. The two-grid method is constructed by first solving the nonlinear system of equations stemming from the discontinuous Galerkin finite element method on a coarse mesh partition; then, this coarse solution is used to linearise the underlying problem so that only a linear system is solved on a finer mesh. Solving the complex nonlinear problem on a coarse enough mesh should reduce computational complexity without adversely affecting the numerical error. We first focus on the a priori and a posteriori error estimation for a scalar second-order quasilinear elliptic PDEs of strongly monotone type with respect to a mesh-dependent energy norm. We then devise an hp-adaptive mesh refinement algorithm, using the a posteriori error estimator, to automatically refine both the coarse and fine meshes present in the two-grid method. We then perform numerical experiments to validate the algorithm and demonstrate the improvements from utilising a two-grid method in comparison to a standard (single-grid) approach. We also consider deviation of the energy norm based a priori and a posteriori error bounds for both the standard and two-grid discretisations of a quasi-Newtonian fluid flow problem of strongly monotone type. Numerical experiments are performed to validate these bounds. We finally consider the dual weighted residual based a posteriori error estimate for both the second-order quasilinear elliptic PDE and the quasi-Newtonian fluid flow problem with generic nonlinearities.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA299 Analysis