A dual-mixed hybrid formulation for fluid mechanics problems: Mathematical analysis and application to semiconductor process technology Original Research Article

In this paper we propose a dual-mixed hybrid formulation capable of treating under a unified framework both compressible and incompressible problems in continuum mechanics. A theoretical analysis of the method is carried out and optimal error estimates are derived for both mixed and hybrid variables. The potentialities of the novel approach are exploited in the computation of the stress field required in the simulation of the thermal oxidation process in semiconductor technology. The numerical formulation is validated both on model problems in continuum mechanics and on a realistic example of the thermal oxidation process in a local oxidation structure.