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1 – 1 of 1Douglas Ramalho Queiroz Pacheco
This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.
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.
Details