A New Minimisation Principle for Poisson Equation Leading to a Flexible Finite Element Approach
For researchers in numerical PDEs, this provides a more flexible finite element approach for solving Poisson equations, though the improvement is incremental.
The paper introduces a new minimisation principle for the Poisson equation that allows flexible finite element discretizations without requiring an inf-sup condition, and demonstrates its superiority with a numerical example.
We introduce a new minimisation principle for Poisson equation using two variables: the solution and the gradient of the solution. This principle allows us to use any conforming finite element spaces for both variables, where the finite element spaces do not need to satisfy a so-called inf-sup condition. A numerical example demonstrates the superiority of the approach.