Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes

Dong, Zhaonan ORCID: https://orcid.org/0000-0003-4083-6593 2019. Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes. International Journal of Numerical Analysis and Modeling 16 (5) , pp. 825-846.

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Abstract

We introduce an hp-version symmetric interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the biharmonic equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, the stability and hp-version a-priori error bound are derived based on the specific choice of the interior penalty parameters which allows for edges/faces degeneration. Furthermore, by deriving a new inverse inequality for a special class of polynomial functions (harmonic polynomials), the proposed DGFEM is proven to be stable to incorporate very general polygonal/polyhedral elements with an arbitrary number of faces for polynomial basis with degree p = 2, 3. The key feature of the proposed method is that it employs elemental polynomial bases of total degree Pp, defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. A series of numerical experiments are presented to demonstrate the performance of the proposed DGFEM on general polygonal/polyhedral meshes.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	ISCI-INST SCIENTIFIC COMPUTING
ISSN:	1705-5105
Date of First Compliant Deposit:	22 January 2020
Last Modified:	17 Nov 2024 03:45
URI:	https://orca.cardiff.ac.uk/id/eprint/128693

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