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finite element method; convection-diffusion equation; stability; inf-sup condition; stabilization; SUPG method; local projection method; error estimates
We consider the local projection finite element method for the discretization of a scalar convection-diffusion equation with a divergence-free convection field. We introduce a new fluctuation operator which is defined using an orthogonal $L^2$ projection with respect to a weighted $L^2$ inner product. We prove that the bilinear form corresponding to the discrete problem satisfies an inf-sup condition with respect to the SUPG norm and derive an error estimate for the discrete solution.
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