Dirichlet degrees of freedom need not be eliminated

Abstract

Dirichlet degrees of freedom are often eliminated from discretized initial value boundary value equations. This has advantages (creation of a symmetric system of equations and simplification of the equations) and a potential disadvantage (modification of the equations could lead to a more complex and less convenient implementation). This paper demonstrates that no elimination is needed to keep all elimination-related advantages – if one uses standard iterative solution techniques in a proper manner.