Summary.
We develop the general a priori error analysis of residual-free bubble finite element approximations to non-self-adjoint elliptic problems of the form \((\varepsilon A + C)u = f\) subject to homogeneous Dirichlet boundary condition, where A is a symmetric second-order elliptic operator, C is a skew-symmetric first-order differential operator, and \(\varepsilon\) is a positive parameter. Optimal-order error bounds are derived in various norms, using piecewise polynomial finite elements of degree \(k\geq 1\).
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Received October 1, 1998/ Revised version received April 6, 1999 / Published online January 27, 2000
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Brezzi, F., Marini, D. & Süli, E. Residual-free bubbles for advection-diffusion problems: the general error analysis. Numer. Math. 85, 31–47 (2000). https://doi.org/10.1007/s002110050476
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DOI: https://doi.org/10.1007/s002110050476