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2 results on '"ZHAONAN DONG"'

1. Recovered finite element methods on polygonal and polyhedral meshes

Author

Emmanuil H. Georgoulis, Tristan Pryer, and Zhaonan Dong

Subjects
Numerical Analysis, Polynomial, Series (mathematics), Applied Mathematics, Degrees of freedom (statistics), 010103 numerical & computational mathematics, 01 natural sciences, Finite element method, 010101 applied mathematics, Computational Mathematics, Discontinuous Galerkin method, Modeling and Simulation, Applied mathematics, Polygon mesh, Boundary value problem, 0101 mathematics, Element (category theory), Analysis, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics
Abstract

Recovered Finite Element Methods (R-FEM) have been recently introduced in Georgoulis and Pryer [Comput. Methods Appl. Mech. Eng. 332 (2018) 303–324]. for meshes consisting of simplicial and/or box-type elements. Here, utilising the flexibility of the R-FEM framework, we extend their definition to polygonal and polyhedral meshes in two and three spatial dimensions, respectively. An attractive feature of this framework is its ability to produce arbitrary order polynomial conforming discretizations, yet involving only as many degrees of freedom as discontinuous Galerkin methods over general polygonal/polyhedral meshes with potentially many faces per element. A priori error bounds are shown for general linear, possibly degenerate, second order advection-diffusion-reaction boundary value problems. A series of numerical experiments highlight the good practical performance of the proposed numerical framework.

Published
2020

2. hp-VERSION DISCONTINUOUS GALERKIN METHODS FOR ADVECTION-DIFFUSION-REACTION PROBLEMS ON POLYTOPIC MESHES.

Author

CANGIANI, ANDREA, ZHAONAN DONG, GEORGOULIS, EMMANUIL H., and HOUSTON, PAUL

Subjects
*GALERKIN methods, *FINITE element method, *APPROXIMATION theory, *COMPUTATIONAL complexity, *POLYGONALES, *POLYHEDRAL functions
Abstract

We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, 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. The proposed method employs elemental polynomial bases of total degree p (Pp-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. 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 employing a (mapped) Qp-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes. [ABSTRACT FROM AUTHOR]

Published
2016
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