A new minimization principle for the Poisson equation leading to a flexible finite element approach

Bishnu Prasad Lamichhane

Abstract


A new minimization principle for the Poisson equation using two variables – the solution and the gradient of the solution – is introduced. This principle allows us to use any conforming finite element spaces for both variables, where the finite element spaces do not need to satisfy the so-called inf–sup condition. A numerical example demonstrates the superiority of this approach.


doi:10.1017/S144618111700030X

Keywords


Poisson equation, minimization principle, mixed finite element method, a priori error estimate.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.11889



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.