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Title: Discontinuous Galerkin Methods on Polytopic Meshes
Authors: Dong, Zhaonan
Supervisors: Georgoulis, Emmanuil
Award date: 3-Jan-2017
Presented at: University of Leicester
Abstract: This thesis is concerned with the analysis and implementation of the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) on computational meshes consisting of general polygonal/polyhedral (polytopic) elements. Two model problems are considered: general advection-diffusion-reaction boundary value problems and time dependent parabolic problems. New hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration as well as an arbitrary number of faces and hanging nodes per element. The proposed method employs elemental polynomial bases of total degree p (Pp- bases) defined in the physical coordinate system, without requiring mapping from a given reference or canonical frame. A series of numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a Pp-basis on both polytopic and tensor-product elements with a (standard) DGFEM and FEM employing a (mapped) Qp-basis. Moreover, a careful theoretical analysis of optimal convergence rate in p for Pp-basis is derived for several commonly used projectors, which leads to sharp bounds of exponential convergence with respect to degrees of freedom (dof) for the Pp-basis.
Type: Thesis
Level: Doctoral
Qualification: PhD
Rights: Copyright © the author. All rights reserved.
Description: File under embargo until 3rd June 2017.
Appears in Collections:Leicester Theses
Theses, Dept. of Mathematics

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