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

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