A multi-point constraint unfitted finite element method

Freeman, Brubeck Lee 2022. A multi-point constraint unfitted finite element method. Advanced Modeling and Simulation in Engineering Sciences 9 , 19. 10.1186/s40323-022-00232-w

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Abstract

In this work a multi-point constraint unfitted finite element method for the solution of the Poisson equation is presented. Key features of the approach are the strong enforcement of essential boundary, and interface conditions. This, along with the stability of the method, is achieved through the use of multi-point constraints that are applied to the so-called ghost nodes that lie outside of the physical domain. Another key benefit of the approach lies in the fact that, as the degrees of freedom associated with ghost nodes are constrained, they can be removed from the system of equations. This enables the method to capture both strong and weak discontinuities with no additional degrees of freedom. In addition, the method does not require penalty parameters and can capture discontinuities using only the standard finite element basis functions. Finally, numerical results show that the method converges optimally with mesh refinement and remains well conditioned.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Publisher:	SpringerOpen
Funders:	EPSRC
Date of First Compliant Deposit:	22 September 2022
Date of Acceptance:	20 August 2022
Last Modified:	07 Jun 2023 22:40
URI:	https://orca.cardiff.ac.uk/id/eprint/152787

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