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Bubble functions prompt unusual stabilized finite element methods. (English) Zbl 1067.76567
Summary: A second-order linear scalar differential equation including a zeroth-order term is approximated using first the standard Galerkin method enriched with bubble functions. Static condensation of the bubbles suggests 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
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