Very weak finite element methods: discretisation and applications
Abstract
Purpose
This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.
Design/methodology/approach
We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.
Findings
Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.
Originality/value
This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.
Keywords
Citation
Ramalho Queiroz Pacheco, D. (2024), "Very weak finite element methods: discretisation and applications", Engineering Computations, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/EC-10-2023-0699
Publisher
:Emerald Publishing Limited
Copyright © 2024, Emerald Publishing Limited