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hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems

Giani, S.

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Abstract

This paper presents a new way to enrich finite element methods with nonpolynomial functions without adding any function to the finite element space. For this reason, the method is called celatus, which is a Latin word meaning ``hidden from view."" Since no nonpolynomial function is added to the finite element space, many issues with standard enriched methods are avoided, among which there is the worsening of the condition of the linear system. In the present work, we focus on second-order elliptic source problems with reentering corners and show that the new method is more computationally efficient than standard finite element methods when used with hp-adaptivity.

Citation

Giani, S. (2018). hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems. SIAM Journal on Scientific Computing, 40(5), B1391-B1418. https://doi.org/10.1137/17m1149912

Journal Article Type Article
Acceptance Date Aug 20, 2018
Online Publication Date Oct 16, 2018
Publication Date Oct 16, 2018
Deposit Date Aug 21, 2018
Publicly Available Date Nov 14, 2018
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 40
Issue 5
Pages B1391-B1418
DOI https://doi.org/10.1137/17m1149912
Public URL https://durham-repository.worktribe.com/output/1322669

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