An approach using the null space to implement Dirichlet and constraint boundary conditions into FEM

Abstract

A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling boundary constraints within FEM simulations for teaching. It presents a consistent way of including the boundary terms in the forcing and constructing the field solution after solving the algebraic system of equations.