The extended spectral element method for the approximation of discontinuous functions

Phillips, Timothy Nigel ORCID: https://orcid.org/0000-0001-6455-1205 and Rowlatt, Christopher Frederick 2014. The extended spectral element method for the approximation of discontinuous functions. Siam Journal on Numerical Analysis

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Abstract

Abstract. High-order polynomial approximations of discontinuous functions give rise to oscillations in the vicinity of the discontinuity known as Gibbs phenomenon. Enrichment of the basis using discontinuous functions is shown to remove these oscillations and to recover the convergence properties generally associated with the spectral approximation of smooth functions. The convergence properties of the enriched method, known as the extended spectral element method (XSEM) are studied and optimal error estimates are derived. The extension of these ideas to the immersed boundary method (IBM) is considered. The IBM is typically used for problems with an interface or discontinuity that is unfitted to the underlying computational mesh. An extended basis is used to approximate the pressure and the implication of this for the inf-sup for the Stokes problem is investigated.

Item Type:	Article
Date Type:	Submission
Status:	Submitted
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0036-1429/ (accessed 26.11.14).
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1429
Funders:	EPSRC
Date of First Compliant Deposit:	30 March 2016
Last Modified:	17 Nov 2023 02:57
URI:	https://orca.cardiff.ac.uk/id/eprint/67801

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