Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear PDEs
Publication Date
July 10, 2014
Creator
Abstract
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.
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
13944
UoN Repository URI
Except where otherwise noted, this item's license is described as
File(s)![Thumbnail Image]()
Name
Congreve_PhD.pdf
Type
Full-text
Size
5.01 MB
Format
Adobe PDF
Checksum ()