BUBBLE FUNCTIONS PROMPT UNUSUAL STABILIZED FINITE-ELEMENT METHODS

A second-order linear scalar differential equation including a zero-th order term is approximated using first the standard Galerkin method enriched with bubble functions. Static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations. The method is generalized to allow for a convection operator in the equation. This work may be employed as a starting point for simulation of non-linear equations governing turbulence phenomena, flows with chemical reactions, and other important problems.