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A Celatus method for the efficient solution of linear elastic problems with re-entrant corner singularities [dataset] Open Access

This paper presents an enrichment method for the case of re-entrant corner singularities in linear elastic problems but with no enrichment of the finite element solution space. Instead an a posteriori error estimator, with gradient descent, is used to determine the approximate solution of the coefficients for the enrichment functions about each re-entrant corner. The method then approximately removes the singularities from the problem, increasing its regularity. As a result is that exponential convergence of the error can be achieved with uniform refinement in polynomial order. Almost no improvement in the error is expected or observed if uniform refinement in p is used. The approach is termed the Celatus method as the singularities are hidden from view. As problems are made regular it is shown that exponential convergence rates are observed when the Celatus method is combined with hp-adaptivity (hp-Celatus), requiring far fewer degrees of freedom compared, by orders of magnitude, to traditional finite element analysis with hp-adaptivity. Furthermore each term for the enrichment functions for every re-entrant corner can be evaluated independently. Therefore the method can be implemented in an inherently parallel way. The proposed approach offers an approximately 10 times reduction in computation time for the same accuracy compared to standard finite element analysis with hp-adaptivity. Additionally, since the solution space is not enriched and is always polynomial, the issue of having near singular matrices does not exist for the Celatus method. The discontinuous Galerkin finite element method is used here, but all equations and methodology are equally applicable to the continuous Galerkin method.

Descriptions

Resource type

Dataset

Contributors

Creator: Bird, Robert E. ¹
Contact person: Bird, Robert E. ¹
Data collector: Bird, Robert E. ¹
Data curator: Bird, Robert E. ¹
Editor: Bird, Robert E. ¹
Editor: Giani, Stefano ¹
Editor: Coombs, William M. ¹

¹ Durham University, UK

Funder

Engineering and Physical Sciences Research Council [EP/W000970/1]

Research methods

Other description

Keyword

enriched method
hp-adaptivity
discontinuous Galerkin
fracture

Subject

Galerkin methods

Location

Language

Cited in

Identifier

ark:/32150/r18g84mm34d
doi:10.15128/r18g84mm34d

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

File Details

Depositor

R.E. Bird

Date Uploaded

24 March 2026, 12:03:02

Date Modified

24 March 2026, 15:03:11

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File format: zip (ZIP Format)

Mime type: application/zip

File size: 10398

Last modified: 2026:03:24 12:09:16+00:00

Filename: celatus_paper_data.zip

Original checksum: deecc8866be15d8f539f9a0c255137a3